The deal is pending medical reviews.
Alex Verdugo will be the centerpiece of the trade coming back to Boston.
The move clears $59 million in 2020 salaries for Boston, with Price due $32 million and Betts $27 million, though the Red Sox are expected to send money to the Dodgers in the deal. The pitcher joined the Red Sox in 2015 from the Tampa Bay Rays. The Red Sox will also be paying a significant portion of Price's remaining three-year, $96 million contract. The third team involved in the trade is believed to be the Minnesota Twins, according to various reports.
Throughout the winter, Boston entertained offers for Betts, whose free-agent haul following the 2020 season could exceed $400 million. Price, a 34-year-old left-hander who is a former Cy Young Award victor, still has three years and $96 million left on the seven-year, $217 million deal he signed in December 2015.
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Maeda, a Japanese native, has spent his entire career in the Major League Baseball with the Los Angeles Dodgers.
Maeda, 31, finished 10-8 with a 4.04 ERA in 37 games (26 starts) previous year in his fourth season with the Dodgers.
Verdugo didn't play after August 4 because of a back injury he re-aggravated while on a rehab assignment in September. Betts was named the 2018 AL MVP and has spent the entirety of his six-year career in Boston.
The Dodgers already looked like one of the favorites to win the World Series this season, but those odds just got even better with the arrival of Betts.