Neither team has announced the deal, which is expected to be official on Friday.
Forsythe, 27, has played parts of the past three seasons with the Padres, hitting .241/.310/.349 in 228 Major League games. He batted .214 with six home runs and 19 RBIs in 75 games last season with San Diego.
Torres was impressive in 39 relief appearances with Tampa Bay last season, posting a 1.71 ERA over 58 innings. The 26-year-old likely will join recently signed closer Joaquin Benoit to fortify the Padres' bullpen.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.