Crisp told MLB.com earlier this month that he expects to be at full strength for the start of Spring Training.
"I'm not worried about the capability of playing 100 percent as far as the season goes," he said.
A veteran of eight big league seasons with the Royals, Red Sox and Indians, Crisp has a .277 lifetime average and .377 on-base percentage to go along with 59 homers, 327 RBIs and 137 steals in 832 games.
The addition of Crisp will likely force incumbent center fielder Rajai Davis, who batted .305 in 125 games with the A's last season, to move to one of the corner outfielder spots.
The Padres, White Sox and Cubs also reportedly had interest in Crisp.
Ed Eagle is a reporter and producer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.