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To make room for Bastardo on the 40-man roster, right-hander Carlos Torres was designated for assignment.
The 30-year old reliever was one of the best arms still on the free-agent market, and the Dodgers, Blue Jays and Orioles were also reportedly interested in his services.
Pitching for the Pirates last season, Bastardo appeared in 66 games and posted a 2.98 ERA over 57 1/3 innings.
Bastardo gives the Mets another lefty in the bullpen mix. Prior to Bastardo's signing, Sean Gilmartin was the club's only healthy lefty.
Additionally, the Mets have Josh Edgin, who is recovering from Tommy John surgery, and Jerry Blevins, who signed a one-year deal in December and is expected to be healthy for the start of the season.
William Boor is a reporter for MLB.com. Follow him on Twitter at @wboor. This story was not subject to the approval of Major League Baseball or its clubs.