The New York-based chain has secured the former KFC site at 1-2 Coventry Street, which is understood to be opening later this year.
It is also believed to be in talks to acquire the Canteen restaurant in Canada Square, Canary Wharf, according to BigHospitality’s sister site MCA.
Shake Shack launched in the UK in Covent Garden in 2013 and currently runs three London sites and one in Cardiff.
Speaking to BigHospitality earlier this year Shake Shack’s culinary director Mark Rosati said the group enjoyed the competition of London’s booming burger market.
“What makes us different is that we’re born out of fine dining…London is a very saturated market but there’s no stopping it because people like a burger,” he said.
“All ships rise with the tide, so if some other guy opens up and starts doing great burgers then it’s just going to re-spark everyone’s love affair with it.”
Rosati creates special menu items for each store including a custard made with Welsh cakes in Cardiff, and a brownie from St John in London.
Shake Shack was launched by US restaurateur Danny Meyer as a food cart in New York’s Madison Square Park in 2004.
It now operates nearly 100 locations worldwide as part of Meyer’s Union Square Hospitality Group.
BigHospitality has contacted Shake Shack for further comment.