He made his debut for Fulham on 21 November 1987 in a 2–0 victory over Rotherham United. After joining the club as a centre-back, Eckhardt gradually adapted to several different positions and became known for his versatility, playing as both a midfielder and a forward during his time at Craven Cottage. He went on to make over 250 appearances for Fulham in all competitions, during a six-year spell at the club and was appointed club captain. At the end of the 1993–94 season, the team suffered relegation to the Third Division and Eckhardt decided to accept an offer from Stockport County manager Danny Bergara. During his time at Stockport, he won promotion to the First Division. He scored his only career hat-trick for the club during a match against Lincoln City, a game in which he also played in goal after an injury to their goalkeeper.