The deal includes an invitation to Milwaukee's big league camp.
Willis, 33, won the National League Rookie of the Year award with the Florida Marlins in 2003 and finished second to St. Louis' Chris Carpenter in the 2005 NL Cy Young Award balloting after posting a 22-10 record. He gained a devoted following through his energetic persona, unorthodox motion and colorful nickname, the "D-Train.''
But Willis quickly faded after coming to Detroit with Miguel Cabrera in a blockbuster trade in 2007. Since 2010, he has pitched for the Diamondbacks, Giants (twice), Reds, Phillies, Orioles, Cubs and Angels organizations and made several stops in independent ball.
Willis' last appearance on a big league mound came four years ago, when he went 1-6 with a 5.00 ERA in 13 starts with Cincinnati. He also batted a career-best .387 (12-for-31) with a home run and four RBIs that season with the Reds. He has a career batting average of .244.
Willis said in a phone conversation Wednesday that he has never contemplated quitting.
"I've been asked that question before, and it all comes down to the fact that I enjoy being on the field,'' Willis said. "I suck at golf. I don't have an Xbox, and I have four daughters. I just love the camaraderie of baseball. Even when I'm done playing, I'll be coaching. I'll get a fungo bat, and I'll be even louder than I am now.''
Willis credited one of his agents, Jon Pridie, with arranging a workout for big league clubs Tuesday in Phoenix. He auditioned for teams at the EXOS sports training facility, where he works out with Jacoby Ellsbury, Edwin Jackson, Casper Wells and several other current and former big leaguers.
Sosnick said that Willis had scanned the rosters of all 30 MLB clubs in hopes that he would attract interest from Arizona or Milwaukee, two teams that train near his home in Phoenix and appear to have an opening for left-handed relief help. Although the Diamondbacks didn't call, Sosnick said Willis received multiple minor league offers before signing with Milwaukee.
"I feel like a rookie,'' Willis said. "This is very humbling. It's going to seem surreal until I see my name on a uniform in spring training. I just can't believe it.''