Wolff played three years of college soccer at the University of South Carolina, where he scored 21 goals and eight assists in 43 games, while playing with another future United States national team star in Clint Mathis. After his junior season, Wolff signed with MLS, and was assigned to the Chicago Fire. He would set the MLS rookie record (together with Jeff Cunningham, since broken by Damani Ralph) by scoring eight goals, doing so in just 14 games (only four of those starts). Wolff would play the next four seasons for the Fire, scoring 24 goals, developing a reputation as one of the league's most explosive offensive players, but unfortunately also one of its most injury prone. Before the 2003 MLS Superdraft, Wolff was traded by the Fire in a cost-cutting move to the Kansas City Wizards in exchange for the third overall pick, which the Fire would use to select Nate Jaqua. In 2003, Wolff lived up to his reputation, missing most of the season due to injuries, but was very productive for an excellent Wizards team in 2004, finishing the year with ten goals and seven assists. He scored ten goals and ten assists in 2005.

Wolff starred for the US in the 2000 Summer Olympics, scoring two goals en route to a fourth-place finish. Josh is among the first-choice forwards for the United States national team and has scored nine goals in 45 caps since his debut against Jamaica on September 8, 1999. As with his club teams, however, Wolff has had trouble securing a definite spot because of continual injury problems. He did play for the United States in the 2002 World Cup, assisting on the opening goal in the second-round win against Mexico. On May 2, 2006, for the second time in his career, Wolff was named to the US roster for the FIFA World Cup in Germany.