Three Boston Red Sox coaches, including Maine native Brian Butterfield, have signed on with other teams, it was announced Thursday.

Butterfield, Boston’s third base coach and infield instructor, and hitting coach Chili Davis will hold the same positions with the Chicago Cubs. Pitching coach Carl Willis is now the Cleveland Indians’ pitching coach.

All three were given permission to look for new jobs after Manager John Farrell was fired two weeks ago. President Dave Dombrowski said he would recommend all the coaching staff to return, but it would be up to Alex Cora, the new manager.

Butterfield, 60, was one of the first coaches hired by Farrell when he was named manager before the 2013 season.

Davis, 57, joined the staff before the 2015 season, and Willis, 56, joined in May of that year, replacing the fired Jan Nieves.

Butterfield was born in Bangor and currently resides in Standish. He graduated from Orono High School and played baseball for the University of Maine, a team his late father (Jack) used to coach.

After a five-year minor league career, Butterfield became a coach in the Yankees organization. He earned a reputation as an infield guru and is credited with turning a raw, young infielder named Derek Jeter into a Gold Gove shortstop.

Butterfield coached on the major league staffs of the Yankees and Diamondbacks before joining the Blue Jays in 2002. He stayed with Toronto until coming over to Boston.

With Boston, Butterfield helped develop Xander Bogaerts into an All-Star shortstop, and worked his magic with Hanley Ramirez, when Ramirez moved to first base in 2016.

Among the remaining Red Sox coaches, only bullpen coach Dana LeVangie has reportedly been offered a job with Boston. LeVangie has been with the Red Sox organization for 26 years as a player, scout and coach.

Assistant pitching coach Brian Bannister is also a team vice president in charge of pitching development, a promotion made by Dombrowski. His job seems secure. The future of the other Boston coaches is unknown. They are bench coach Gary DiSarcina, first base coach Ruben Amaro, and assistant hitting coach Victor Rodriguez.

Cora will not be formally introduced as the Red Sox manager until his duties as bench coach of the Houston Astros are over, after the World Series.