Terms of the contracts weren't disclosed.
"I'm more than happy and I'm excited to be back!" Garnett told reporters.
The 36-year-old averaged 15.8 points and 8.2 rebounds over 60 games in his fifth season with the Celtics last year.
"We are ecstatic that Kevin will continue his career with the Celtics," added Celtics President of Basketball Operations Danny Ainge. "Kevin has greatly changed the culture since he first put on a Celtics jersey and he has come to embody everything that we want in a Celtic."
Seventh-year pro Bass recorded averages of 12.5 points and 6.2 rebounds last season, while Wilcox, 29, compiled 5.4 points and 4.4 rebounds in 28 games before undergoing surgery for an enlarged aorta in the lockout-shortened 2011-12 season.