The jointly branded venue will be open to eaters and internet surfers alike within a few weeks. EasyInternetCafe branding will appear on the outside of the building and in the windows, and the upstairs seating area will be devoted to the internet cafe. PCs will also be dotted about in the main restaurant downstairs.
An easyGroup spokesman said: "If Burger King want to leave their branding up then that is fine with us."
He said the Burger King partnership, and a similar initiative at McDonald's Swiss Cottage restaurant, were easyInternetCafe's first steps to expansion since the retrenchment sparked by the bursting of the dotcom bubble.
He said the strategy was for "one-step growth through franchising and use of existing real estate".
If the Piccadilly experiment is a success, the concept will be rolled out to other Burger King outlets.
"We are very conscious of the fact the Burger King has 600 restaurants in the UK, several hundred more in Europe and several thousand more in the US."
The tie-up is the second manifestation of a growing friendship between the burger restaurant and easyGroup owner Stelios Haji-Ioannou, which began when the entrepreneur starred in a Burger King radio ad this week.
In the ad, which promoted BK's new Swiss Melts, Stelios bemoaned the fact that Burger King customers could get a taste of Switzerland for just £1.49 when easyJet's cheapest flight to Switzerland cost £30.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum here.