The National League champions announced the move Thursday.
The 33-year reliever spent last season in the Milwaukee Brewers' minor league system, the majority of the year with Triple-A Colorado Springs.
Henderson made his major league debut with the Brewers in 2012 after nine years in the minors. In three big league seasons he's made 111 relief appearances, going 8-9 with 31 saves and a 3.44 ERA.
A 26th-round draft pick of the Montreal Expos in 2003, Henderson's best season came in 2013, when he had 28 saves and made 61 appearances.