The deal with Tazawa, an indispensable part of Boston's bullpen the last three seasons, is for $2.25 million.
That leaves lefty Wade Miley and outfielder Daniel Nava as the club's two remaining arbitration-eligible players.
Miley, who came to the Red Sox in a trade from the D-backs back in December, submitted an arbitration figure of $4.3 million while Boston countered at $3.4 million.
Nava is requesting $2.25 million while the Red Sox submitted an offer of $1.3 million.
The Red Sox have not had an arbitration hearing with a player since Rolando Arrojo in 2002.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.