The 32-year-old made 62 starts for the Brewers in his career, posting a 4.99 ERA in 2010 and a 4.45 ERA in 2011. But in 2012, after only two starts, Narveson tore his rotator cuff which ultimately ended his season. He made two appearances out of the bullpen last season before landing on the disabled list again.
During his rehab assignment with Triple-A Nashville, Narveson accumulated a 7.00 ERA in five starts, forcing the Brewers to remove him from the 40-man roster. He finished the season with a 4-7 record and a 5.14 ERA in 15 starts with the Sounds.
This winter, Narveson pitched in the Dominican Winter League and boasted a 1.98 ERA. Along with the Swallows, Narveson also drew interest from the Houston Astros.