Drew, who spent one season in Boston, turned down a $14.1 million offer from the Red Sox last year after helping the team capture their third title in 10 years.
He reportedly accepted a one-year deal that will pay him approximately $10 million.
We have the ability, provided all things work out, we've added a very good player to improve this team," Boston manager John Farrell said Tuesday before the Red Sox hosted the Toronto Blue Jays. "That's the thing (GM) Ben (Cherington) and ownership have repeatedly shown — when a need exists, they'll do whatever is capable and whatever is available to improve the team.
"Stephen's return to us could very well do that. It will add stability to the left side of the infield."
The 31-year-old will take a physical Wednesday and assuming he passes, will require minor-league stint before joining the Red Sox. Once he is ready, Drew will take over at shortstop and rookie Xander Bogaerts will be shifted to third base.
Third baseman Will Middlebrooks was placed on the disabled list Saturday with a fractured right index finger.
"We had a chance to sit and talk with Xander," Farrell said. "He's aware of everything that's been talked about and reported, and just wanted to be a little bit ahead of things, as to what it might mean to his position going forward."
The move comes as the Red Sox have lost four straight games, their longest skid since dropping their final eight of the 2012 season.
Drew batted .253 with 13 home runs and 67 RBIs in 124 games with Boston last season.