Azzuri, which is behind the Zizzi, Coco di Mama and ASK Italian brands, invested in the concept in 2016.
Radio Alice is the brainchild of brothers Salvatore and Matteo Aloe, who run 12 pizzerias in Italy under the Berberè brand.
The first Radio Alice opened in Hoxton in 2016 and it has been followed by two further sites in Clapham and Canary Wharf.
The Aloe brothers are now relocating to the UK to take full control of the company's day-to-day operations.
Matteo and Salvatore say: “We started with just one pizza oven, a collective of farmers and a young team in our hometown of Bologna. Our aim is to create quality sourdough pizza using the very best seasonal ingredients, offering the best quality pizza to everyone, and we hope that today’s deal allows us to continue our adventure in London.
“We would like to thank Azzurri Group and [Radio Alice managing director and Gail’s co-founder] Emma King for enabling us to open in a city we love – after three successful years of our joint venture, we look forward to continuing our love affair with London. “