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.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Couple mistakenly served bag of cash at McDonald's drive-thru