In return for Montero, the Cubs sent right-handed pitchers Jeferson Mejia and Zack Godley to the Diamondbacks.
Montero, 31, is a .264 career hitter with a .763 OPS over parts of nine seasons in Arizona. He made the National League All-Star team in 2011 and 2014. He is in the middle of a five-year, $60 million contract and has $40 million owed to him over the next three seasons.
The Montero trade marks another move in an already busy offseason for the Diamondbacks, who have already acquired pitcher Jeremy Hellickson from Tampa Bay in a trade, sent shortstop Didi Gregorius to the New York Yankees and signed Cuban outfielder Yasmany Tomas to a six-year, $68.5 million contract as a free agent.
Trade talks between the Cubs and Diamondbacks appeared to hit a lull late Monday night, according to a person familiar with the discussions, but Chicago ratcheted up its offer to bring the deal to fruition.
The Cubs recently hired former Arizona coach Henry Blanco, and he is expected to continue to mentor Montero on the defensive side during the catcher's transition to Chicago. Montero improved his pitch-framing last season and threw out almost 30 percent of runners attempting to steal.
Montero, a left-handed hitter, brings an offensive upgrade to a Chicago catching contingent that ranked 21st in the majors with a .684 OPS last season. Montero could be part of a platoon in Chicago with Welington Castillo, a righty bat who hit .301 with an .855 OPS against lefties in 2014.
The 20-year-old Mejia went 2-4 with a 2.48 ERA in 12 games (two starts) for the Cubs' rookie league affiliate in Mesa. A native of the Dominican Republic, this was his first year pitching in the United States after signing with Chicago as an undrafted free agent.
Godley, 24, was 4-3 with 15 saves and a 3.09 ERA in 40 appearances for Chicago's Class A affiliates in Kane County and Daytona. The former University of Tennessee pitcher was a 10th-round selection by the Cubs in the 2013 draft.