Zambrano, 30, waived his full no-trade clause in order to complete the deal, FOX Sports reported.
The Cubs are expected to pay between $15 million and $16 million of the $18 million Zambrano is guaranteed in 2012. Zambrano, who was 9-7 with a 4.82 ERA in 24 starts last season, will become a free agent next winter.
The Cubs placed the volatile pitcher on the restricted list in 2010 and disqualified list in 2011 due to issues with his temperament. Zambrano walked out on his teammates in August following a clubhouse blowup in Atlanta after getting ejected from a game.
New Cubs president Theo Epstein said Thursday he did not want to be quick to judge Zambrano, but came to the determination after talking to other players that the right-hander lost the "trust" of his teammates.
"I was skeptical," Epstein told the Chicago Tribune. "I'm not big on labels, I'm not big on reputations dictating how I treat people or how I think about people.
"But this was one that was really consistent. Every player I talked to articulated to me that Carlos really violated their trust. When you're talking about physical altercations with players repeatedly, when you're talking about physically walking out on the team, it's very hard to then have that player come back into the clubhouse and be trusted."
In return for parting ways with Zambrano, the Cubs add Volstad, who in four seasons with the Marlins amassed a 4.59 ERA. The towering right-hander -- standing six-foot-eight -- is expected to garner $2.5 to $3 million in arbitration, which will be subtracted from the $18 million Chicago owed Zambrano.