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Concentration of Risk and Segment Data - Segment Revenue and Income (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
May 31, 2019
May 31, 2018
May 31, 2019
May 31, 2018
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Net revenue $ 6,135,602 $ 5,436,952 $ 18,708,867 $ 16,323,585
Reconciling items:        
Amortization of intangibles (7,610) (10,040) (23,033) (29,909)
Stock-based compensation expense and related charges (14,506) (15,038) (47,452) (82,822)
Restructuring and related charges (9,340) (12,647) (16,182) (29,462)
Other expense (14,084) (10,139) (39,391) (26,506)
Interest income 6,758 4,499 15,897 13,323
Interest expense (50,514) (36,178) (139,326) (110,220)
Income before income tax 83,078 71,153 348,791 264,854
Cayey, Puerto Rico        
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Insurance recoveries   5,000 2,900 21,400
EMS        
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Net revenue 3,988,489   11,296,319  
Reconciling items:        
Restructuring and related charges (7,600) (4,600) (12,300) (12,600)
DMS        
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Net revenue 2,147,113   7,412,548  
Reconciling items:        
Restructuring and related charges 0 (5,800) (2,100) (13,800)
Operating Segments        
Reconciling items:        
Income before income tax 185,765 150,062 630,484 555,878
Operating Segments | EMS        
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Net revenue 3,988,489 3,161,626 11,296,319 8,894,174
Reconciling items:        
Income before income tax 130,869 121,563 303,618 302,556
Operating Segments | DMS        
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items]        
Net revenue 2,147,113 2,275,326 7,412,548 7,429,411
Reconciling items:        
Income before income tax 54,896 28,499 326,866 253,322
Segment Reconciling Items        
Reconciling items:        
Distressed customer charge 0 0 0 (14,706)
Stock-based compensation expense and related charges (14,506) (15,038) (47,452) (82,822)
Acquisition and integration charges (13,391) 0 (35,066) 0
Business interruption and impairment charges, net(1) $ 0 $ 634 $ 2,860 $ (10,722)