Narveson, 31, will attempt to reclaim his spot in the Brewers rotation after missing most of 2012 with a torn rotator cuff. He only appeared in two games last year and went 1-1 with a 7.00 ERA in nine innings of work.
In the previous two seasons, Narveson made 56 starts for the Brewers. He went 12-9 with a 4.99 ERA over 167⅔ innings in 2010. In 2011, he went 11-8 with a 4.45 ERA in 161⅔ innings.
The left-hander is 26-18 with a 4.67 ERA over 394⅔ in five seasons spent with the Brewers and the St. Louis Cardinals.
Narveson will join the rotation which includes Yovani Gallardo, Marco Estrada and Mike Fiers.
The Brewers now have four players who are arbitration eligible in John Axford, Burke Badenhop, Marco Estrada and Carlos Gomez.