The deal was announced Saturday.
Rogers split time last season with Cleveland and Colorado, going 3-3 with a 4.69 ERA in 67 combined games. The 27-year-old is 11-12 lifetime in the majors with a 5.95 ERA.
Aviles never played for Toronto. He was acquired on Oct. 21 in a deal that sent reliever David Carpenter to the Red Sox and allowed John Farrell to become Boston's new manager.
The 31-year-old Aviles played in 136 games for Boston last season, batting .250 with 13 homers and 60 RBIs.
Gomes played 43 games with Toronto last season, his first in the majors. He hit .204 with four home runs and 13 RBIs.