"I feel relieved," said Masao Matsui. "I didn't think it would be decided so quickly. I'm eager to see his play in a new environment and can't wait to see the new Matsui."
The New York Times reported on Monday the Major League Baseball teams had agreed a trade worth $6.5 million.
Matsui batted .274 with 28 homers and 90 RBIs for the New York Yankees last season, the last of his four-year $52 million contract with the Bronx Bombers.
The powerful left-hander was voted World Series MVP last month despite starting only three of the six games against Philadelphia.
Matsui went 8 for 13 (.615) with three homers and eight RBIs, tying a Series record by driving in six runs in Game 6.
The designated hitter had expressed his hope to remain a Yankee but has undergone surgery on both knees, slowing him to the degree that he no longer plays in the outfield.
(Reporting by Alastair Himmer, editing by Nick Mulvenney)