Tom Alexander, who will leave the chief executive role on 31 August, said he wished "to pursue other interests".
He will be replaced by Olaf Swantee, who is currently executive vice president at France Telecom.
Everything Everywhere is a joint venture between Deutsche Telekom and France Telecom.
It started operations in May 2010 when the two companies merged their UK operations.
Telecoms analysts have questioned whether the merger has been carried out as smoothly as had been intended.
Mr Alexander was Everything Everywhere's first chief executive. He had previously held the same position at Orange UK from 2008.
"It's been my privilege to serve Everything Everywhere these past twelve months, and Orange before that," he said.
"Olaf will be an excellent chief executive and leader for Everything Everywhere moving forward."
Mr Alexander will continue in an advisory role at the company until the end of the year.
Mr Swantee is already on the board of Everything Everywhere. Prior to joining France Telecom, he worked for computer maker HP.
Everything Everywhere is the UK's largest mobile phone network operator, with about 28 million customers across the Orange and T-Mobile brands. It has 16,000 employees and 700 stores.
Its number of new contract customers slowed in the first quarter of 2011.
The boss of Everything Everywhere, the parent group of UK mobile phone networks Orange and T-Mobile, is standing down for "personal reasons".