The Wales international moved to South London from Tottenham Hotspur in January and made 26 appearances in all competitions.
Among Johnson’s total were seven appearances for Palace in the UEFA Conference League last season, which culminated in the Eagles lifting silverware at the culmination of a first-ever major European campaign.
Chairman Steve Parish said: “Everyone at the club would like to thank Brennan for his contribution towards our successful second half of last season.
“We wish him the very best of luck in all his endeavours in the future.”