The rebuilding Indians received right-hander Justin Masterson and minor league pitchers Nick Hagadone and Bryan Price. The trade came shortly before the 4 p.m. ET deadline to complete deals without waivers.
Prior to officially acquiring Martinez, Boston spun off first baseman Adam LaRoche and cash in a trade with his former team, the Braves. LaRoche, who was acquired from Pittsburgh for prospects on July 22, returns to Atlanta in exchange for first baseman Casey Kotchman.
The 30-year-old Martinez has split his time at catcher and first base this season. The switch-hitter is batting .284 with 15 home runs and 67 RBIs.
Martinez, who had spent his whole career with Cleveland, fought back tears after being told he'd been traded. He sat in front of his locker, hugging son Victor Jr. -- earlier in the day, the young boy asked his dad, "Are we still an Indian?"
"It's tough," Martinez said. "This is my house. This is my home."
Martinez leaves Cleveland a day before the Indians were to hold Victor Martinez Bobblehead Night at Progressive Field in their game against Detroit.
He'll move right into a pennant race with Kotchman, joining a Red Sox team that is second in the AL East behind the New York Yankees, but leads the wild-card chase.
"You've been traded already so you're a little more used to it," Kotchman said. "I'm a little surprised but not overwhelmingly surprised."
Kotchman is hitting .282 with six homers and 41 RBIs and hasn't committed an error in his two seasons with the Braves.
"It's been a privilege to play for Bobby Cox and his staff," Kotchman said.
Cleveland, which began the weekend 12 games out of first in the AL Central, has slashed nearly $25 million in payroll by trading Lee, Martinez, third baseman Mark DeRosa, reliever Rafael Betancourt and first baseman Ryan Garko.
"When you don't perform or have good results, things are going to happen like this," Indians center fielder Grady Sizemore said. "It's start from scratch now."
Martinez will likely share catching duties in Boston with Jason Varitek and can fill in at first base and designated hitter.
The Red Sox did not give up Clay Buchholz, one of their top pitching prospects, for Martinez. But they did part with three quality arms in order to bolster their lineup.
The versatile Masterson was Boston's second-round pick in 2006. He went 3-3 with a 4.50 ERA in 31 appearances, including six starts for the Red Sox this season. The 6-foot-6 righty was a key part of the Red Sox's run to the playoffs a year ago, going 6-5 with a 3.16 ERA in 36 games after being called up from the minors.
The 23-year-old Hagadone, a 6-foot-5 lefty, has pitched sparingly since being drafted No. 55 overall by the Red Sox in 2007. He missed much of the 2008 season after having Tommy John surgery and has worked only 25 innings this year, going 0-2 with a 2.52 ERA at Class A Greenville.
Price was drafted 45th overall in 2008. The 22-year-old righty has struggled in his first two years of pro ball, going just 5-11 with a 4.42 ERA in 31 outings.
The Red Sox held a three-game lead in the AL East at the All-Star break, but a five-game losing streak on the ensuing road trip dropped them into second place behind the rival Yankees.
Boston has won only four of its past 12 games, has a losing record on the road and five of its starting nine are batting .250 or below.
Boston general manager Theo Epstein has already been active this month: He traded for LaRoche, sent shortstop Julio Lugo to St. Louis for minor leaguer Chris Duncan, and got outfielder Brian Anderson from the Chicago White Sox for infielder Mark Kotsay.
Information from The Associated Press was used in this report.