Fulham reported Liverpool to the Premier League this summer after the west London club became annoyed at the Reds' bid to sign Dempsey.
The row started when a story appeared on the Fenway Sports Group website, claiming the United States international had joined Liverpool.
Reds boss Brendan Rodgers then admitted enquiring about the forward, but failed to follow it up with a concrete bid, much to the annoyance of Martin Jol, who claimed Liverpool had unsettled the forward with their "embarrassing" conduct.
Fulham initially decided to press ahead with their complaint to the Premier League despite the fact that Dempsey eventually joined Tottenham, but on Wednesday they decided to forget the matter after Liverpool chairman Tom Werner apologised to his Fulham counterpart Mohamed Al Fayed.
A statement on Fulham's website read: "Fulham can confirm that it has today withdrawn the complaint made against Liverpool FC in regard to the Merseyside club's inappropriate actions surrounding interest in Clint Dempsey over the summer.
"Liverpool's chairman Tom Werner apologised personally to Mohamed Al Fayed, stating that his club were wholly responsible for unprofessional behaviour toward Fulham and emphasised his regret for the entire episode.
"In a letter from Liverpool to Fulham's CEO Alistair Mackintosh, Tom Werner's praise of the magnanimous gesture from the chairman was reiterated, as was the club's assurance that the conduct of Liverpool was simply not acceptable.
"The chairman decided that this sincere action was enough, and as a gesture of goodwill, instructed that all complaints against them be dropped."
- Sports & Recreation