Commitments, Contingencies and Off-Balance Sheet Arrangements - Contractual Obligations (Detail) $ in Millions	Sep. 30, 2021 USD ($)
Senior Notes [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, Thereafter	$ 850.0
Contractual Obligations, Payments Due by Period, Total	850.0
Note Purchase Agreements [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2022	200.0
Contractual Obligations, Payments Due by Period, 2023	250.0
Contractual Obligations, Payments Due by Period, 2024	475.0
Contractual Obligations, Payments Due by Period, 2025	200.0
Contractual Obligations, Payments Due by Period, Thereafter	3,323.0
Contractual Obligations, Payments Due by Period, Total	4,448.0
Premium Financing Debt Facility [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	234.1
Contractual Obligations, Payments Due by Period, Total	234.1
Interest On Debt [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	59.9
Contractual Obligations, Payments Due by Period, 2022	217.7
Contractual Obligations, Payments Due by Period, 2023	208.7
Contractual Obligations, Payments Due by Period, 2024	192.0
Contractual Obligations, Payments Due by Period, 2025	177.4
Contractual Obligations, Payments Due by Period, Thereafter	1,406.9
Contractual Obligations, Payments Due by Period, Total	2,262.6
Total Debt Obligations [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	294.0
Contractual Obligations, Payments Due by Period, 2022	417.7
Contractual Obligations, Payments Due by Period, 2023	458.7
Contractual Obligations, Payments Due by Period, 2024	667.0
Contractual Obligations, Payments Due by Period, 2025	377.4
Contractual Obligations, Payments Due by Period, Thereafter	5,579.9
Contractual Obligations, Payments Due by Period, Total	7,794.7
Operating Lease Obligations [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	21.8
Contractual Obligations, Payments Due by Period, 2022	102.0
Contractual Obligations, Payments Due by Period, 2023	81.9
Contractual Obligations, Payments Due by Period, 2024	59.5
Contractual Obligations, Payments Due by Period, 2025	45.5
Contractual Obligations, Payments Due by Period, Thereafter	88.2
Contractual Obligations, Payments Due by Period, Total	398.9
Less Sublease Arrangements [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Receivable by Period, 2021	(0.3)
Contractual Obligations, Payments Receivable by Period, 2022	(0.8)
Contractual Obligations, Payments Receivable by Period, 2023	(0.6)
Contractual Obligations, Payments Receivable by Period, 2024	(0.3)
Contractual Obligations, Payments Receivable by Period, 2025	(0.2)
Contractual Obligations, Payments Receivable by Period, Thereafter	(0.5)
Contractual Obligations, Payments Receivable by Period, Total	(2.7)
Outstanding Purchase Obligations [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	33.5
Contractual Obligations, Payments Due by Period, 2022	68.9
Contractual Obligations, Payments Due by Period, 2023	47.3
Contractual Obligations, Payments Due by Period, 2024	30.7
Contractual Obligations, Payments Due by Period, 2025	22.9
Contractual Obligations, Payments Due by Period, Thereafter	37.4
Contractual Obligations, Payments Due by Period, Total	240.7
Total Contractual Obligations [Member]
Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]
Contractual Obligations, Payments Due by Period, 2021	349.0
Contractual Obligations, Payments Due by Period, 2022	587.8
Contractual Obligations, Payments Due by Period, 2023	587.3
Contractual Obligations, Payments Due by Period, 2024	756.9
Contractual Obligations, Payments Due by Period, 2025	445.6
Contractual Obligations, Payments Due by Period, Thereafter	5,705.0
Contractual Obligations, Payments Due by Period, Total	$ 8,431.6

Commitments Contingencies And Off Balance Sheet Arrangements [Line Items]

No definition available.

Name:	ajg_CommitmentsContingenciesAndOffBalanceSheetArrangementsLineItems
Namespace Prefix:	ajg_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Recorded unconditional purchase obligation due after fourth year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationDueAfterFourthYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivable
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable after fifth year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableAfterFifthYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable in fifth year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableInFifthYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable in fourth year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableInFourthYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable in second year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableInSecondYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable in third year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableInThirdYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Recorded unconditional purchase obligation receivable within one year.

+ References

No definition available.

+ Details

Name:	ajg_RecordedUnconditionalPurchaseObligationReceivableWithinOneYear
Namespace Prefix:	ajg_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of the recorded obligation to transfer funds in the future for fixed or minimum amounts or quantities of goods or services at fixed or minimum prices (for example, as in take-or-pay contracts or throughput contracts).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 440
-SubTopic 10
-Section 50
-Paragraph 6
-URI http://asc.fasb.org/extlink&oid=123406679&loc=d3e25383-109308

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligation
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of recorded unconditional purchase obligation to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationDueInFourthYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of recorded unconditional purchase obligation to be paid in remainder of current fiscal year.

+ References

No definition available.

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationDueInRemainderOfFiscalYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of recorded unconditional purchase obligation to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationDueInSecondYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of recorded unconditional purchase obligation to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationDueInThirdYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of recorded unconditional purchase obligation to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationDueWithinOneYear
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_NotePurchaseAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_PremiumFinancingDebtFacilityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_InterestOnDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_DebtObligationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_OperatingLeaseObligationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_SubleaseArrangementsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_OutstandingPurchaseObligationsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RecordedUnconditionalPurchaseObligationByCategoryOfItemPurchasedAxis=ajg_ContractualObligationsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: