Soria is 3-1 with a 2.85 ERA in 43 appearances in 2015, with 36 strikeouts and 11 walks in 41 innings for the Tigers. The right-hander has converted 23 of 26 save opportunities this season, though he has also allowed eight home runs.
Soria joins an already-strong relief corps in Pittsburgh, which ranks second among National League bullpens in ERA (2.71) and third in strikeout-to-walk ratio (2.91).
Pirates closer Mark Melancon has a 1.32 ERA and leads the National League with 32 saves, with 33 strikeouts and 10 walks in 47⅔ innings.
The 31-year-old Soria is under contract for $7 million in 2015, with roughly $2.5 million remaining the rest of the season. Soria will be a free agent after 2015.
Soria is the second free-agent-to-be traded by the Tigers on Thursday. Detroit sent pitcher David Price to the Toronto Blue Jays for three minor league players on Thursday morning.