Welsch has played in the National Basketball Association in the United States, having been drafted in 2002 by the Philadelphia 76ers.

Welsch began his professional career as a teenager with BK JIP Pardubice of the Czech Republic League, where he played until 1998.

[2] Without ever playing a game for them, Welsch, along with Mills, Raef LaFrentz and a lottery-protected 2004 NBA draft pick, was traded by Dallas to the Boston Celtics on 20 October 2003 in exchange for Antoine Walker and Tony Delk.

The Bucks would lose the game 93–122 and drop the series to Detroit 4–1, with Welsch recording 2 points, 1 assist and 1 rebound.

In August 2006, Welsch decided to leave the NBA, and he signed with the Spanish ACB league club Unicaja Málaga.