The family-run sandwich business, which has three sites across Bristol, will take over the former Tossed site at the junction of Gresham Street and St Martins Le Grand.
News of Sandwich Sandwich's first London site comes after the business, which is led Josh Kleiner, was named the Uber Eats UK and Ireland's Restaurant of the Year back in October, securing a prize of £100,000 to invest in the business.
“I can't believe this is happening," Kleiner wrote on Instagram.
"I think this is what people would normally describe as a 'pinch-me' moment.
"I honestly can't put into words how excited yet nervous we all are. Naturally, I find myself focusing on the risks involved in making this move, but the love and support we receive on a daily basis tells us this is the right decision to make."
Sandwich Sandwich was founded by Kleiner's father back in 2010 as Gotham Sandwich Co.
It changed its name in 2012 as part of its aims to expand across Bristol and has since opened sites in Baldwin Street, Queens Road and Park Row.
Sandwich Sandwich's menu includes a range of deep-filled sandwiches that are made to order.
Fillings include sliced Southern fried chicken with house coleslaw and spicy Creole sauce; overnight roasted sirloin of beef with red onion, tomato, cheddar and horseradish mayonnaise; and an all day breakfast with bacon, sausage, egg mayonnaise, ketchup and brown sauce.