He'll earn $7.5 million plus incentives, a source told The Athletic's Ken Rosenthal.
The Twins were on the hunt for a second baseman after trading Brian Dozier to the Los Angeles Dodgers last season. They had also been linked to DJ LeMahieu and Jed Lowrie, sources told Jeff Passan of Yahoo Sports.
In 2017, Schoop received MVP consideration after an All-Star campaign for the Orioles. He hit 32 home runs and finished sixth in the American League with 105 RBIs.
The 27-year-old infielder has hit 110 career home runs in 681 games.
Torreyes, 26, has spent the past three seasons with the New York Yankees. He's hit .281/.310/.375 with 56 RBIs in 229 career games with the Yankees and Dodgers.