Lackey had to pass a physical before the deal became official. The team scheduled a 1:30 p.m. ET press conference to announce the signing.
The agreement was first reported by ESPN.com's Jayson Stark.
The deal is worth $82.5 million over five years, sources told ESPN The Magazine's Buster Olney on Tuesday.
Lackey traveled to Boston for a physical exam Monday, fueling speculation that an agreement was close at hand.
The Red Sox's heightened pursuit of Lackey came after reports that Boston is fading in its efforts to retain free-agent outfielder Jason Bay.
The Mariners, Angels and Mets were among the other teams interested in signing Lackey.
Entering the offseason, it was believed that Lackey would use A.J. Burnett's five-year, $82.5 million contract with the New York Yankees as a benchmark, but industry estimates of his potential haul have ranged from $60 million to $100 million.
There were reports that Lackey declined a $72 million offer earlier this year from the Angels, but his representatives have since characterized those reports as untrue.
Lackey shut out the Red Sox through 7 1/3 innings in Game 1 of the AL Division Series and nearly no-hit Boston in 2008, but in nine career regular-season starts at Fenway Park, he is 2-5 with a 5.75 ERA.
Bay turned down Boston's latest contract offer late last week and was ready to "move on" from Boston, according to his agent, Joe Urbon. The Red Sox have no intention of offering Bay a five-year deal, a source told ESPNBoston.com.
In other moves, the Red Sox scheduled an 11:30 a.m. ET press conference for Wednesday to announce a deal with free-agent outfielder Mike Cameron. A source told ESPN.com's Jerry Crasnick it is for two years.
Cameron had to pass a physical exam for the deal to become official.
Also still up in the air is the status of third baseman Mike Lowell, who will undergo a physical for the Rangers this week, a source told ESPNDallas.com, as the Red Sox and Rangers continue to evaluate a proposed trade that would send Lowell to Texas and catcher Max Ramirez to Boston.
Jayson Stark and Jerry Crasnick cover Major League Baseball for ESPN.com.