Boston, which announced the signings Tuesday, also invited all the players to major league spring training.
Carlson appeared in 162 games for the Blue Jays from 2008-10, posting a 3.63 earned run average and 114 strikeouts in 141 1/3 innings. However, the 31- year-old left-hander missed all of last season because of rotator cuff surgery.
Silva played in the Yankees' organization last season, pitching in seven games at three different levels. Prior to 2011, the right-hander was a major league starter and enjoyed moderate success while with the Twins from 2004-07, when he went 47-45 with a 4.42 ERA in 129 games (124 starts).
He has appeared in 316 games over nine major league seasons with Philadelphia, Minnesota, Seattle and the Chicago Cubs.
Duckworth, 35, spent last season with the Red Sox's Triple-A affiliate in Pawtucket and went 8-6 with a 3.97 ERA in 22 games (21 starts). The right- hander last pitched in the majors in 2008, when he was with Kansas City, and has also played for Philadelphia and Houston in eight major league seasons.