Veras was in jeopardy of not being tendered a contract by Monday's midnight ET deadline, while McGehee became expendable after Milwaukee signed free agent Aramis Ramirez to be the club's starting third baseman.
After batting .285 with 23 homers and 104 RBIs in 2010, McGehee endured a tough '11 season, hitting just .223 with 13 homers, 67 RBIs and a .280 on-base percentage. McGehee appeared in 155 games, mostly as the team's starting third baseman.
McGehee's season-long struggles prompted manager Ron Roenicke to replace McGehee with Jerry Hairston Jr. in the starting lineup during the playoffs.
The addition of McGehee, 29, gives the Pirates another option at third base, though the club has insisted that Pedro Alvarez will get the first crack at holding onto the starting role. If the Pirates don't need McGehee to step in and play third, he could be used across the diamond at first base or as a backup outfielder.
McGehee, like Veras, was arbitration-eligible for the first time this offseason. He has played in the National League Central for his entire Major League career. In his first full season in the Majors (2009), McGehee batted .301 with 20 doubles, 16 homers and 66 RBIs in 116 games.
Veras made a career-high 79 appearances for the Pirates in 2011, many of those coming in late-inning setup situations. The 31-year-old right-hander finished with a 3.80 ERA, 79 strikeouts and 34 walks in 71 innings.
Though Veras played a key role in the 'pen last season, the Pirates have enough other internal options to move on without him in the mix. Later on Monday, the club tendered contracts to arbitration-eligible relievers Joel Hanrahan, Evan Meek and Chris Resop. Right-handed reliever Jason Grilli also came to an agreement on a one-year deal with the club on Monday.