Terms of deal weren't disclosed, but MLB.com said the contract also includes a club option for 2015.
Burnett, 30, was a key piece in the Washington Nationals' run to the National League East crown this past season while logging a 2.38 earned run average and striking out 57 in 56 2/3 innings over 70 appearances.
The situational specialist has averaged 7.8 strikeouts per nine innings over the past three seasons with the Nationals.
Former Titans kicker dies in car crash
UPI Sports Results for September 20, 2014