Ken Rosenthal of The Athletic was first to report the agreement.
Nicholson-Smith reports that the Blue Jays are sending No. 2 prospect Austin Martin and No. 4 prospect Simeon Woods Richardson to the Twins in the trade.
Berrios, who is under team control through the 2022 season, was one of the most sought-after starters on the trade market. He has 3.48 ERA and 126 strikeouts in 20 starts for the Twins this season. The two-time All-Star has spent his entire six-year career with the Twins and outside his rookie season he has never had an ERA above 4.00.
The move gives the Blue Jays a third ace starter to join Robbie Ray, Alek Manoah and Cy Young finalist Hyun-Jin Ryu. It also is the latest blockbuster move in the AL East arms race after the Yankees, Red Sox and Rays all made trades in recent days to add power bats to their lineups.
The Blue Jays enter play Friday, their first home game at the Rogers Centre in nearly two years, fourth in the division with a 51-48 record. They are 9.5 games back of the Red Sox for first in the division and 4.5 games out a wild card spot.