The team said it has signed the right-hander to a one-year, minor league deal with an invitation to spring training. He could earn $900,000 if he makes the big league roster.
Colon, 37, didn't pitch in the majors last season. He last appeared in the majors in 12 games for the White Sox in 2009, going 3-6 with a 4.19 ERA.
Colon hasn't made more than 20 starts in a season since 2005, when he won the Cy Young Award with the Angels. He went 21-8 with a 3.48 ERA that season.
In 13 major league seasons with the Indians, Montreal Expos, White Sox, Angels and Red Sox, Colon has a 153-103 record with a 4.10 ERA. He averages 7.0 strikeouts and 3.1 walks per game for his career.
General manager Brian Cashman has said the team is searching for another starter, but he also has called the free-agent market, after Lee, a weak one.