The transmission is the Turbo-Hydramatic 440-T4 aka the 4T60, which was used in:
1985-’90 Cadillac Eldorado, de Ville, Fleetwood (FWD)
1988-’90 Buick Riviera, Reatta
1985-’93 A/C/H body cars (Buick Century, Chevrolet Celebrity, Oldsmobile Cutlass Ciera, Oldsmobile Cutlass Cruiser, Pontiac 6000, Buick LeSabre, Oldsmobile Eighty-Eight, Pontiac Bonneville, Buick Electra)
1988-’94 W body cars (Buick Century, Buick Regal, Chevrolet Impala, Chevrolet Lumina, Chevrolet Monte Carlo, Oldsmobile Cutlass Supreme, Oldsmobile Intrigue, Pontiac Grand Prix)
Some of the C, H, and W cars made after ’91 have the 4T60-E transmission, which is the computer controlled version of your transmission.