The London Premier League club said in a statement on their website they had accepted Welshman Hughes's decision to leave after 43 games in charge.
"Fulham Football Club can confirm that Mark Hughes has provided notice, under the terms of his contract, to leave the club at the end of June," Fulham said on their website.
"After discussions with Mark the club has agreed to accept this notice."
But the former Manchester United, Barcelona and Chelsea striker issued a statement saying he had taken the decision to "further his experiences".
"I would also like to take this opportunity to clarify that neither myself nor my representative have approached or have been approached by another club," the 47-year-old said.
"This decision to leave Fulham has not been influenced by any outside party.
"I would like to thank the chairman, directors, players and fans of Fulham Football Club for their support over the last 12 months and wish them every success in the future," Hughes added.
"I believe my management team and I have done a good job and the club has a strong foundation from which they can go forward."
After taking Wales to the brink of the Euro 2004 finals, Hughes's first Premier League coaching assignment came with Blackburn Rovers, the club where he finished his playing career.
