Correa's deal, which was first reported by Fox 26 Houston, will pay him $35.1 million in each of the three years, sources said.
Correa picking the Twins was a surprise, given they have lost 18 consecutive postseason games and finished last in the AL Central a year ago at 73-89.
A two-time All-Star who was the first pick in the 2012 amateur draft, Correa led the Astros' turnaround. Houston lost more than 100 games each year from 2011-13, then won its first World Series title by beating the Los Angeles Dodgers in seven games in 2017.
He is coming off perhaps his best season, posting a career-best 7.2 WAR, according to Baseball-Reference.com, which ranked third in the American League. He hit .279 with 26 homers, 92 RBIs and 104 runs for the Astros. The oft-injured Correa played in 148 games, his most since the 2016 season.
It was also Correa's most decorated season. He appeared in the All-Star Game, finished fifth in AL MVP balloting, won his first Gold Glove at shortstop and was awarded a Platinum Glove by Rawlings as the AL's top overall defender. Since Correa broke in for the Astros in 2015, he ranks sixth among all position players in WAR (34.1).
For all his regular-season exploits, Correa has been even more accomplished during the postseason. Since his first appearance for Houston in 2015, Correa ranks third among all players in postseason homers (18). His 59 RBIs in the playoffs are 10 more than any other player during that span.
Still, Correa remains a controversial figure because of his association with the sign-stealing scandal that tainted the Astros' 2017 World Series title, and his adamant defense about the legitimacy of the championship. Before the 2020 season, he told reporters, "When you analyze the games, we won fair and square. We earned that championship."
Despite the controversies, Correa is respected around the game as a clubhouse leader.
"If your best player is not a good leader, they can take you down the wrong road," Astros manager Dusty Baker said of Correa during the 2021 playoffs. "Carlos is in the great category."
Moving to the Twins will be a change for Correa and his family. His wife, the former Daniella Rodriguez, was Miss Texas USA in 2016.
Minnesota has not been to the World Series since winning the 1991 title and has lost its past eight postseason series since beating Oakland in a 2002 AL Division Series.
Correa has enjoyed great success in Minnesota as a visiting player, though. He has a .413 batting average (26-for-63) at Target Field with five homers and 20 RBIs in 15 games. His 1.205 OPS is his highest at any ballpark where he has played four or more games.
Before the work stoppage, Minnesota signed pitcher Dylan Bundy to a $5 million, one-year deal.
Correa became a free agent after rejecting the Astros' qualifying offer, worth $18.4 million. As a result of his departure, Houston will recoup a compensatory draft pick.
Correa was the top overall pick of the 2012 amateur draft after being selected by Houston out of the Puerto Rico Baseball Academy. He then went on to win AL Rookie of the Year honors in 2015.
ESPN's Bradford Doolittle and The Associated Press contributed to this report.