"I'm very happy that Matsuzaka's dream of playing in the Major Leagues will be realised," Seibu's acting owner Hidekazu Ota said.
"I told Matsuzaka of the result and he was also very happy."
The battle for the 26-year-old was the subject of intense speculation in the US and Japan over the last month and the Red Sox now have 30 days to strike a deal with Matsuzaka. The New York Yankees and Chicago White Sox were among teams also believed interested in the pitcher.
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The record bid far exceeded expectations and dwarfs the $13 million Seattle paid to negotiate with Ichiro Suzuki, who joined the Mariners in 2001.
Boston will not have to pay the sum if a deal cannot be reached with the right-hander and his agent Scott Boras.
Japanese media reported the pitcher would leave Japan for the United States later on Wednesday.
Matsuzaka can expect to command an annual salary of around $10 million in a multi-year contract with Boston.
The commissioner's office of Major League Baseball simultaneously announced that the Red Sox had made the highest bid during a general managers meeting in Naples, Florida.
"We're excited to have won this part of the process," Red Sox general manager Theo Epstein said.
"We're hopeful we can reach an agreement."
The hard-throwing Matsuzaka, with his mysterious "gyroball" pitch, has a 108-60 career record and an earned-run average of 2.95. He would join a Boston pitching staff featuring Curt Schilling and Josh Beckett.
Matsuzaka spent eight years as Seibu's top pitcher and picked up the MVP award in the inaugural World Baseball Classic in March after leading Japan to the championship.
If Matsuzaka joins the Red Sox he would create an interesting rivalry with New York Yankees' Japanese slugger Hideki Matsui.
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