After graduating from Oak Hills High School, Wegman was drafted by the Milwaukee Brewers in the 5th round of the 1981 amateur draft, where he played throughout his entire 11-year career, ending on October 1, 1995. In 1983, Wegman won the Ray Scarborough Award as the Brewers' Minor League Player of the Year.[2] Wegman won a career-high 15 games in 1991, with a 2.84 earned run average.