The teams announced the trade Monday, saying that Chapman is expected to join the National League-leading Cubs for their game Tuesday against the crosstown rival Chicago White Sox.
The Yankees received a four-player package, headlined by top shortstop prospect Gleyber Torres, in exchange for Chapman, who was suspended for the first 29 games of this season under baseball's domestic violence policy.
"Obviously, we are aware of the circumstances surrounding Aroldis Chapman's suspension earlier this season," Cubs chairman Tom Ricketts said in a statement. "We are also aware that he cooperated fully with the league investigation and takes responsibility for his actions."
Chapman was involved in an October incident when he allegedly choked his girlfriend, but police did not file charges against the Cuban-born left-hander, citing insufficient evidence, conflicting stories and uncooperative witnesses. Major League Baseball announced Chapman's suspension in early March, two months after the Yankees traded four minor leaguers to the Cincinnati Reds for the All-Star closer.
"I want to thank the New York Yankees for trusting and supporting me, and I wish nothing but the best for the Yankees organization and my former teammates," Chapman said in a statement.
Now the five-time All-Star is headed to Chicago, where he figures to bolster a struggling bullpen and strengthen the Cubs' pursuit of their first World Series championship since 1908.
"I am excited about today's trade and look forward to joining the Chicago Cubs and meeting my new teammates," he said. "It is a privilege to wear the Cubs uniform and to play for the fans of Chicago."
Hector Rondon has a 1.95 ERA and 18 saves this season as Chicago's closer, but the rest of the Cubs' bullpen has been spotty. The Cubs had a combined ERA of 3.83, ranking seventh in the NL, entering Monday, when the bullpen gave up a game-winning hit to White Sox shortstop Tyler Saladino in the bottom of the ninth inning of a 5-4 loss.
The Cubs paid a steep price, parting with Torres, versatile pitcher Adam Warren and minor league outfielders Billy McKinney and Rashad Crawford.
But there is no doubting the talent of the 28-year-old Chapman, who went 3-0 with a 2.01 ERA and 20 saves in 31 games with New York. He threw a 105.1 mph fastball to Baltimore's J.J. Hardy last Monday night, matching the fastest since MLB began tracking speeds in 2008.
With lefty-batting sluggers Bryce Harper of Washington and Brandon Belt of San Francisco possibly looming in the playoffs, the addition of Chapman gives Cubs manager Joe Maddon one of the majors' top assets when in need of a late strikeout.
"Today, prior to completing the trade, Theo, Jed and I spoke with Aroldis," Ricketts said. "I shared with him the high expectations we set for our players and staff both on and off the field. Aroldis indicated he is comfortable with meeting those expectations.
"Finally, my family, this team and Major League Baseball take the issue of domestic violence very seriously and support efforts to reduce domestic violence through education, awareness and intervention."
Chapman told police in October that he poked the woman on the shoulder and she fell to the ground. According to the police report, after family members broke up the altercation, Chapman said he went into his car, punched the passenger-side window, and suffered a laceration on his finger. He also acknowledged firing eight shots from a handgun in his garage during the incident.
"I regret that I did not exercise better judgment and for that I am truly sorry," Chapman said in Monday's statement. "Looking back, I feel I have learned from this matter and have grown as a person. My girlfriend and I have worked hard to strengthen our relationship, to raise our daughter together, and would appreciate the opportunity to move forward without revisiting an event we consider part of our past."
Chapman saved 146 games with a 2.17 ERA in six years with the Reds before he was traded to New York last December after a deal with the Los Angeles Dodgers fell through amid reports of the domestic violence incident.
New York had won six of eight games heading into Monday night's game at Houston, but still faces long odds of getting to the playoffs. All-Stars Andrew Miller and Dellin Betances are still at the back of the bullpen, allowing the Yankees to trade Chapman now and still consider trying for the postseason depending on how they fare ahead of the Aug. 1 non-waiver trade deadline.
"This isn't a white flag," Yankees GM Brian Cashman said. "It is a rearrangement."
If New York slips back any further, it could engage in a rare sell-off for the franchise. Miller, who is signed through 2018, also could be traded. Outfielder Carlos Beltran, first baseman Mark Teixeira and pitcher Ivan Nova are eligible for free agency after the season and could be sought by contenders.
Chapman quickly turned into one of baseball's most dominant relievers when he broke into the majors in 2010 with Cincinnati. He threw the 62 fastest pitches in the major leagues last season, ranging from 103.92 to 102.36 mph.
Torres, a 19-year-old at Class A, is the centerpiece of the deal for the Yankees. He is the Cubs' top-ranked prospect and No. 26 in baseball, according to ESPN Insider Keith Law. Torres was scratched about 20 minutes before first pitch Sunday afternoon.
Chicago originally acquired Warren in an earlier trade with the Yankees that sent Starlin Castro to New York. The right-hander went 3-2 with a 5.91 ERA in 29 games this season with the Cubs.
McKinney, 21, is at Double-A. He was part of the 2014 trade that brought Addison Russell to Chicago from Oakland.
ESPN's Jesse Rogers and the Associated Press contributed to this report.