He went 13-6 with a 4.57 ERA in 32 starts in his All-Star season in 2005 with the Boston Red Sox. Clement has not pitched in the majors since 2006 because of shoulder problems.
The 34-year-old Clement is 87-86 with a 4.47 ERA in nine major league seasons with San Diego, Florida, the Chicago Cubs and Boston.
Clement signed a one-year, $1.5 million deal with St. Louis last winter, but was released after 16 minor league appearances, including four starts.
Clement believes he can get back to the major leagues and make a contribution for the Blue Jays.
"I wouldn't be signing a contract with someone if I didn't think I could," Clement said on a conference call after his contract was finalized. "I have three sons and a wife, I'm not going to chase the dream just because I was there before."