Osborne attended Carson High School in Carson City, Nevada before he was drafted by the Montreal Expos in the 1987 Major League Baseball Draft.

After declining to sign with the Expos, Osborne attended the University of Nevada, Las Vegas (UNLV), where he played for the UNLV Rebels baseball team.

Out of UNLV, Osborne was chosen by the St. Louis Cardinals in the first round (13th overall) of the 1990 amateur draft.

In 1996, Osborne won 13 games for the Cardinals, made 30 starts for the only time in his career, pitched 198+2⁄3 innings, and posted a 3.53 earned run average.

He ranked among the National League top-10 in walks per nine innings, shutouts, ERA+, and strike-to-walk ratio.