Goalkeeper Valdes, 34, will be released by Manchester United having played twice in the past 18 months, along with 22-year-old midfielder Nick Powell.
Adebayor, 32, leaves Crystal Palace having signed for the club in January.
Manchester City will let 35-year-old defender Martin Demichelis go after three seasons at the Etihad Stadium, while midfielders Mikel Arteta, 34, Mathieu Flamini, 32, and Tomas Rosicky, 35, will not return to Arsenal next season.
Everton’s released list includes two players who have spent more than 15 years at Goodison Park, 35-year-olds Tony Hibbert and Leon Osman, while Steven Pienaar, 34, brings to an end a second spell with the Toffees.
Goalkeeper Mark Schwarzer, 43, leaves Premier League champions Leicester City, and Stoke City have released 34-year-old striker Peter Odemwingie.
Elsewhere, strikers Steven Fletcher, 29, and Danny Graham, 30, leave Sunderland, along with 36-year-old former England defender Wes Brown.
Clubs have also informed the Premier League of those players who will remain, with Chelsea set to retain 82 players for next season.
For a full list of the Premier League’s retained and released lists, click here.
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