The Japanese star has been on the disabled list since May 18, with the Red Sox saying he had slight tear on his ulnar collateral ligament.
The 30-year-old sought a second opinion in Japan last week and will reportedly tell the Red Sox on Thursday of his decision to undergo the surgery.
The procedure, which transfers a tendon from another part of the body to the elbow, will end Matsuzaka's season and possibly next season as well, meaning he could have played his last game for the Red Sox. His six-year, $52 million deal with the club ends next year.
Matsuzaka won 33 games in his first two years with the Red Sox, but struggled with injuries and inconsistency the past two seasons.