Jackson was drafted in the first round, 32nd overall, in the first-year player draft by the Toronto Blue Jays in 2004 after completing his Junior year at Texas A&M University. He pitched very well, jumping to Triple-A in his first year. At the end of the year, the Blue Jays traded him along with Dave Bush and Gabe Gross to the Brewers for Lyle Overbay and Ty Taubenheim in December 2005.

The Brewers started Jackson playing in Triple-A for the Nashville Sounds at the beginning of 2006. Jackson pitched well and had a 3.00 ERA for the first month and a half. The Brewers called Jackson up on June 2 to help with their current pitching problems. Jackson filled a major void left by the injured Tomo Ohka, replacing him in the starting lineup. He fared much better than expected and was sent back down to Triple-A to fine-tune his game, where he spent the entire 2007 season.

On July 7, 2008, Jackson was part of the deal that sent Cy Young award winner CC Sabathia to Milwaukee for left fielder Matt LaPorta, pitcher Rob Bryson and Michael Brantley. Jackson was recalled in August 2008 to fill the starting pitcher spot vacated by recently traded Paul Byrd.

...
Wikipedia