The Red Sox announced the signing on Wednesday, after Drew underwent a physical.
"I think Stephen helped us out a lot last year," said designated hitter David Ortiz. "Great player, great teammate and hopefully he brings the same attitude that he had last year and helps us win some games."
Before Drew makes his debut for Boston in 2014, he will need a Minor League rehab assignment of roughly 25 at-bats, according to manager John Farrell.
Rookie Xander Bogaerts, who has been the starting shortstop through the early part of the season, will move to third base once Drew is activated. Third baseman Will Middlebrooks is on the disabled list for the second time this season after fracturing his right index finger last week.
When Middlebrooks returns, he could at least start at third base against lefties, with Bogaerts supplanting Drew at short for many of those games.
The Red Sox had a 20-23 record entering Tuesday's game with the Blue Jays.
"Provided everything works out [with the physical], we've added a very good player to improve this team," said Farrell. "That's the one thing that [general manager] Ben [Cherington] and ownership have repeatedly shown -- when a need exists, they'll do whatever is capable and available at a given time to improve the team. Stephen's return to us could very well do that. It'll add stability to the left side of the infield."
Drew came to the Red Sox as a free agent in 2013 and played in 124 games, hitting .253 with 13 homers, 67 RBIs and a .777 OPS. He helped stabilize the left side of the infield with solid defense that was particularly evident in October, when the Red Sox went on to win the World Series.
The one-year contract means Drew can become a free agent again at the end of this season. The Red Sox will not have to surrender a Draft pick because Drew was their own free agent. The fact that other teams would have had to provide the Red Sox with a compensation pick by signing Drew was perhaps the main reason he still remained available until Tuesday.
"We're looking for ways to improve this team," Farrell said. "Without having to give up talent to acquire a good player in Stephen, we were able to sign him as a free agent. Once he gets back to us, we'll add a good player to this team."
With Drew en route back to Boston, Kendrys Morales is the one prominent free agent who remains on the market.
Bogaerts played third base after making his Major League debut last season, starting there for the final eight games of the postseason.
Middlebrooks is batting .197 in 21 games.
"We've got to get Will healthy first, and we've got to get Will back to game speed," Farrell said. "Until that happens, we'll factor all that in once he does return to us."
And after weeks of speculation, Drew will at last return. And one of the first things he'll likely do is collect his World Series ring.
"Any time you sign a good player, it's a positive thing," said right fielder Shane Victorino. "He's a guy who has been here before, a guy who was part of that championship team."