
<PAGE>   1
                                                                   EXHIBIT 99.1 



                                                                November 1, 1995
 
                            USA WASTE SERVICES, INC.
 
                              NOTICE OF REDEMPTION
 
              8 1/2% CONVERTIBLE SUBORDINATED DEBENTURES DUE 2002
 
        CONVERSION PRIVILEGE EXPIRES AT 5:00 P.M. (EASTERN TIME) AT THE
                    PLACE OF CONVERSION ON DECEMBER 1, 1995
 
     NOTICE IS HEREBY GIVEN that, at 5:00 p.m. on December 11, 1995 (the
"Redemption Date"), pursuant to Section 1205 of the Indenture dated as of
September 1, 1992 (the "Indenture"), between USA Waste Services, Inc. (the
"Company") and State Street Bank and Trust Company as successor to The First
National Bank of Boston, as Trustee, the Company will redeem all of its
outstanding 8- 1/2% Convertible Subordinated Debentures Due 2002 (the
"Debentures"), at a redemption price of $1,056.67 plus accrued interest of
$13.46 from October 15, 1995, to the Redemption Date, for a total of $1,070.16
for each $1,000 principal amount of Debentures (the "Redemption Price"). The
Redemption Price will be due and payable on each $1,000 principal amount of
Debentures on the Redemption Date (unless the Debentures are converted as
referred to below). From and after the Redemption Date, interest thereon shall
cease to accrue, and holders of Debentures will not have any rights as such
holders other than the right to receive the Redemption Price, without interest,
upon surrender of their Debentures.
 
                ALTERNATIVES AVAILABLE TO HOLDERS OF DEBENTURES
 
HOLDERS OF DEBENTURES HAVE THE FOLLOWING ALTERNATIVES:
 
     1. Conversion. Prior to 5:00 p.m. (Eastern time) on December 1, 1995, to
convert any or all of the Debentures into the Company's Common Stock at a
conversion price of $13.25 per share (75.472 shares of Common Stock for each
$1,000 principal amount of Debentures). Holder's will receive a cash payment in
lieu of any fractional share. The method of delivery is at the option and risk
of the holder but, if mail is used, it is recommended that registered mail with
return receipt requested, properly insured, be used as a prevention against
loss. If conversion is being requested, Debenture certificates should be mailed,
together with a Letter of Transmittal, sufficiently in advance of December 1,
1995, to permit delivery to the Trustee on or before such date and time.
 
     2. Redemption. To surrender Debentures for redemption at the total
Redemption Price of $1,070.16 for each $1,000 principal amount of Debentures.
 
     3. Sale Through Ordinary Brokerage Transactions. To sell the Debentures
through open market brokerage transactions and, if made sufficiently in advance
of December 1, 1995, buyers thereof may convert the Debentures into Common Stock
in the manner described herein. After December 1, 1995, a holder of Debentures
will not be entitled to convert such Debentures into Common Stock. This is
expected to have an impact on the market for the Debentures. Holders of
Debentures who wish to make sales should consult with their brokers concerning
if and when such Debentures should be sold.
 
     Instructions on presentation of Debentures for conversion or redemption are
given on the accompanying Letter of Transmittal.
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     In order to be converted into Common Stock, the Debentures must be
presented, surrendered and received before 5:00 p.m. (Eastern time) on December
1, 1995, to State Street Bank and Trust Company at one of the following
addresses, where they may also be surrendered for redemption:
 
<TABLE>
<S>                                           <C>
        By Mail or Overnight Courier:                            By Hand:
         State Bank and Trust Company                         Chemical Bank
    Corporate Trust Department, 4th Floor           A/C State Street Bank & Trust Co.
           Two International Plaza                     Ground Floor/Receive Window
               Boston, MA 02110                              4 New York Plaza
                                                            New York, NY 10004
</TABLE>
 
     For the convenience of holders of Debentures, a form of Letter of
Transmittal, which may be used for forwarding Debentures for conversion or for
redemption by the Company, has been mailed to each record holder of Debentures
and to nominees for holders of Debentures to be forwarded to each holder with a
copy of this notice, together with a copy of a Prospectus relating to Common
Stock issuable by the Company to Sanders Morris Mundy Inc., as standby purchaser
in respect of Debentures not converted by the holders thereof into shares of
Common Stock on or before December 1, 1995. Additional copies of the form of
Letter of Transmittal and the Prospectus may be obtained from the Company, 5400
LBJ Freeway, Suite 300 -- Tower One, Dallas, Texas 75240, Attn: Ms. Kay
Stockler, (214) 383-7900.
 
     THE LAST REPORTED SALE PRICE OF THE COMMON STOCK ON OCTOBER 30, 1995, WAS
$20.75 PER SHARE. AT SUCH LAST REPORTED SALE PRICE PER SHARE, THE HOLDER OF
$1,000 PRINCIPAL AMOUNT OF DEBENTURES WOULD RECEIVE, UPON CONVERSION, 75 SHARES
OF COMMON STOCK AND CASH IN LIEU OF A FRACTIONAL SHARE HAVING AN AGGREGATE
MARKET VALUE OF APPROXIMATELY $1,566.03. SUCH VALUE IS SUBJECT TO CHANGE
DEPENDING ON CHANGES IN THE MARKET PRICE OF THE COMMON STOCK. SO LONG AS THE
MARKET PRICE OF THE COMMON STOCK IS AT LEAST $14.18 PER SHARE, HOLDERS OF
DEBENTURES WHO CONVERT THEIR DEBENTURES INTO COMMON STOCK WILL RECEIVE COMMON
STOCK HAVING A GREATER MARKET VALUE (WITHOUT TAKING INTO CONSIDERATION SALES
EXPENSE) THAN THE CASH WHICH THEY WOULD RECEIVE UPON REDEMPTION.
 
     Please be sure to read and follow the instructions on the Letter of
Transmittal.
 
     If there are any questions concerning this matter, please contact either
State Street Bank and Trust Company (617) 664-5419 or USA Waste Services, Inc.
at (214) 383-7900.
 
                                            USA WASTE SERVICES, INC.
 
                                            By:   JOHN E. DRURY,
                                               Chairman of the Board and Chief
                                                  Executive Officer
