Wheeler gets a $1 million buyout and Aybar a $275,000 buyout. Both become free agents.
Aybar batted .230 with six homers and 43 RBIs in 100 games this year. His 10 RBIs as a pinch-hitter this season were the most by an AL player since 2004.
Wheeler is a veteran of 11 major league seasons who has spent parts of seven seasons with the Rays. He went 2-4 with three saves and a 3.35 ERA in 64 games in 2010.
Tampa Bay also selected the contract of utilityman Elliot Johnson from Triple-A Durham on Wednesday.