The Daily Telegraph reports that the deal has been agreed with the 4G provider and that the stadium will now be known as "Wembley Stadium in association with EE," "Wembley Stadium supported by EE" or another similar construction.
The paper reported that the FA hoped to raise £8 million-a-year for the naming rights to the ground.
Such deals have increased in recent seasons in the UK with Manchester City's Eithad Stadium and Arsenal's Emirates among the more high profile examples.
However, football has become the first of the country's big three team sports the sell the naming rights to their HQ venue.
Lord's for cricket and Twickenham for rugby have not sold, nor sought, any naming rights, although The Oval, which has also hosted many of England's Tests matches, has had three difference names since first selling their naming rights and is currently called the Kia Oval.
The FA sees the Wembley deal as similar to the one they currently have for the FA Cup which is officially known as the FA Cup sponsored by Budweiser.
Wembley itself also has a number of commercial deals but until now, no lead sponsor.
EE was formed in 2010 after a merger between Orange and T-Mobile.