Farrell takes over from Bobby Valentine, who lasted just one sub-par season as the Bosox manager.
"This is an incredible privilege to be standing here today," said Farrell, who had been considered for the job last year.
Farrell, 50, returned to Boston from Toronto where he went 154-170 in two seasons. He previously was the Red Sox' pitching coach for four years. As a player, he pitched for the Cleveland Indians, California Angels, and Detroit Tigers, compiling a 36-46 record with a 4.56 earned run average.
He was given a three-year contract by Boston General Manager Ben Cherington. The Red Sox also obtained pitcher David Carpenter from Toronto and sent shortstop Mike Aviles to the Blue Jays as part of the deal.
Farrell said while he's familiar with the Red Sox roster, "it will be my approach to start to earn that trust and re-establish those relationships."
"Because I've been here before, there will be no taking for granted that relationships will exist," he said.
"I still think there is a very good core group of players here. We do need some work in the rotation. The capability is here and we need to get guys healthy."