He was released along with misfiring Morroccan forward Marouane Chamakh and Norwegian defender Brede Hangeland.
Adebayor joined Palace on a short-term deal in January but netted just once in his 15 appearances for the club.
Chamakh too failed to nail down a starting spot during his two years at Selhurst Park and was not help by injuries, which restricted the Morocco international to just 66 appearances.
Hangeland, who featured just 26 times over the course of the last two seasons, will be joined by fellow defender Adrian Mariappa in leaving the club.
The London club have also cut ties with long-serving defender Paddy McCarthy, who made 151 appearances since arriving back in 2008.
Staying for another season, however, are goalkeeper Julian Speroni and defender Damien Delaney who both signed one-year contract extensions.