Atchison will report to major league spring training camp, where he'll have a chance to win a spot in Cleveland's bullpen. The 37-year-old appeared in 50 games for the Mets last season, interrupted by two trips to the disabled list. He became a free agent last month when New York failed to offer a 2014 contract.
The right-hander's best season was 2012, when he had a 1.42 ERA in 42 games for Boston. Atchison has a 10-10 record with one save and a 3.64 ERA in 205 major league appearances. He also has pitched for Seattle, San Francisco and Hanshin in Japan's Central League.
The Indians need help in the bullpen after losing Joe Smith and Matt Albers in free agency. They also released closer Chris Perez and extended a non-roster invite to free agent OF Jeff Francoeur, signing him to a minor league contract.
Francoeur, who turns 30 on Wednesday, will report to spring training camp in Arizona, where he'll try to win a job on Cleveland's 25-man roster. A .263 career hitter, Francoeur nearly signed with the Indians four years ago.
He played with Kansas City and San Francisco last season, batting a combined .204 with three homers and 17 RBIs in 81 games. Francoeur has driven in at least 75 runs four times, and he won a Gold Glove with Atlanta in 2007.
Francoeur has 140 career homers and 618 RBIs in 1,227 games for the Braves, Mets, Rangers, Royals and Giants. He was drafted in the first round in 2002 by Atlanta.
The Associated Press contributed to this report.