Brasier is starting Tuesday's game against the Giants, Jack Harris of the Los Angeles Timesreports.
Brasier signed a two-year, $9 million contract with the Dodgers on Monday, Ken Rosenthal of The Athletic reports.
Brasier earned a hold against the Nationals on Friday, striking out one batter in a perfect inning.
The Dodgers selected Brasier's contract from Triple-A Oklahoma City, Fabian Ardaya of The Athletic reports.
Brasier said Monday that he has agreed to a minor-league contract with the Dodgers, Rob Bradford of WEEI.com reports.
Brasier was released by the Red Sox on Sunday, Christopher Smith of The Springfield Republican reports.
Brasier allowed three runs on one hit and two walks while striking out one over two-thirds of an inning in Saturday's 8-7 extra-inning win over Cleveland.
Brasier picked up the save during Sunday's 2-1 win over the Angels, striking out one over a perfect ninth inning.
Brasier allowed a hit and a walk while striking out one over a scoreless eighth inning to earn his first hold in Thursday's 6-3 win over Detroit.
Brasier signed a one-year, $2 million contract with the Red Sox on Friday, avoiding arbitration, Alex Speier of The Boston Globe reports.