The $3.9 million deal, which includes $100,000 in incentives, was first reported by CBS Sports' Jon Heyman.
Bailey reportedly asked for $4.7 million in arbitration, while Boston offered $3.35 million, putting the agreed upon deal's value close to the midpoint.
Bailey's contract represents a considerable savings compared to Jonathan Papelbon, whom Bailey succeeds after Papelbon left for Philadelphia on a four-year, $50 million deal.
Boston has two arbitration-eligible players who remain unsigned: David Ortiz, who's been reported to want a multiyear deal, and Alfredo Aceves. Big Papi, who made $12.5 million last year, asked for $16.5 million in his arbitration filing, while the Red Sox have countered at $12.65 million. Aceves, who proved invaluable as a swing man for the Sox last season, submitted an arbitration figure of $1.6 million. Boston's figure is $950,000.
Bailey joins Jacoby Ellsbury, Daniel Bard, Mike Aviles, Jarrod Saltalamacchia, Ryan Sweeney and Franklin Morales in inking one-year deals and avoid arbitration.
Salary arbitration hearings would be held from Jan. 31-Feb. 21 in St. Petersburg.