Allen is currently the pitching coach for the Triple-A Durham Bulls in the Tampa Bay Rays' system, a position he's held for the past four years. He's been with the Rays organization since 2007.
Allen was chosen over the other finalist, former Cleveland and Seattle pitching coach Carl Willis, according to the Star Tribune.
Allen, 56, pitched 11 seasons in the major leagues from 1979-1989 with the Mets, Cardinals, White Sox, Yankees and Indians.
He couldn't immediately be reached for comment Saturday.
Allen had a phone interview on Monday with Twins general manager Terry Ryan and manager Paul Molitor, according to the Pioneer Press, and related to them his experience with the Tampa Bay organization.
“We don’t have a monster payroll, so we’ve got to build from within,” Allen told the paper Thursday. “We can’t go out and compete with Boston and New York in the free-agent market. We’ve got to produce in our farm system."
Allen has a good reputation for getting the farm system to produce. He's helped Tampa Bay develop a strong pitching staff that has kept the Rays in contention each year despite the low payroll, according to the Star Tribune.
Allen replaces Rick Anderson, who was the Twins pitching coach for 13 seasons under former manager Ron Gardenhire. He was dismissed when Gardenhire was fired as manager in late September.
Other coaches already hired for Molitor's staff are hitting coach Tom Brunansky, assistant hitting coach Rudy Hernandez and third-base coach Gene Glynn.
Former Twins closer Eddie Guardado will reportedly become the team's bullpen coach, but that move has not yet been announced.
The team still needs a bench coach and a first-base coach to round out the staff.