Los Angeles will send $1.8 million of the $3.6 million remaining on Kinsler's contract, according to Rosenthal, and Boston will trade away LHP Williams Jerez and RHP Ty Buttrey in return for the second baseman.
Kinsler, 36, has maintained his production level from 2017 when he was with the Tigers. He was traded by Detroit in December. In 91 games with Los Angeles entering Monday, he has a slash line of .239/.304/.406 to go along with 13 home runs, 20 doubles and 32 RBIs.
Boston has seen Eduardo Nunez and Brock Holt get time at second this season, but neither has been able to provide the power to the order that Kinsler has displayed so far this season. Nunez has six homers in 336 at-bats and Holt has just one dinger in 197 at-bats.
Kinsler is in his 13th season. The four-time All-Star spent eight years with the Rangers at the start of his career and then four with the Tigers prior to this season.
The Red Sox have the best record in baseball at 75-33 and hold a six-game edge over the Yankees in the AL East after Monday's extra-inning win over the Philies.