"This is all part of the club's ambition to ensure that it is set up to deliver long-term sporting success," the Premier League club said in a statement on its website on Thursday.
Levy, known for his tough negotiating style, has often been a source of frustration for fans who blame him for failing to pay the wages that would deliver players capable of delivering Tottenham's first English top-flight title since 1961.
But he has also been responsible for transforming the club with a new stadium and a state-of-the-art training ground.
Last season, under Postecoglou, Spurs beat Manchester United to win the Europa League, their first trophy since 2008, putting them in the lucrative Champions League for the seventh time under Levy.
But following their worst ever season in the Premier League, finishing 17th, he was still ruthless enough to sack Postecoglou and replace him with Thomas Frank - his 13th full-time managerial appointment at Spurs.
"I am incredibly proud of the work I have done together with the executive team and all our employees," the 63-year-old Levy, the longest-serving chairman in the Premier League, said.
"We have built this club into a global heavyweight competing at the highest level. I wish to thank all the fans that have supported me over the years. It hasn't always been an easy journey but significant progress has been made."
Tottenham said there were no changes to the ownership or shareholder structure of the club.
Levy took over as chairman from Alan Sugar in February 2001 after ENIC bought a majority stake in the club.
During his time in the role Spurs have won only two trophies, the League Cup and the Europa League .
Peter Charrington, a director of ENIC, takes over in the newly-created role as non-executive chairman, the club said.
Spurs are ranked ninth on the Forbes soccer rich list with an estimated value of $US3.3 billion ($A5.1 billion).Â
