Weston, who has been head chef at Phil Howard's the Square for 16 years, will head up the kitchen at the Michelin-starred La Trompette when the restaurant will reopen later this month after a refurbishment.
La Trompette has been closed since the beginning of the year for an expansion into the building next door. Owners Nigel Platts-Martin and Bruce Poole have bought the shop next door, which has resulted in the extension of the kitchen as well as the expansion of the dining room and the creation of a new private dining facility.
Poole said: "We bought the shop next door on Devonshire Road and have put in a brand new kitchen. We've created a private dining facility for minimum 14 guests and expanded the dining room, which means the restaurant now has a total capacity of about 95 covers."
He added: "Rob is busy writing his menus at the moment and we will reopen with his menus at the end of this month. It will be a similar format to what we were doing before and menus will be priced £45 for three courses at dinner."
Meanwhile Howard said Weston's departure marked a "sad day" for the Square. "Rob walked through the doors of The Square, fresh from a stint in Australia, 22 years ago and was instrumental in helping forge the restaurants early reputation," he said.
"Ambition took him to a string of world-class restaurants before returning in 1998. Since then he has run the kitchen in his own inimitable style! Yes, the Square has lost a phenomenal cook, a mighty leader and he leaves a might big pair of shoes to fill. Personally I have lost a soul mate, a partner in crime and a rock of great support. The Square will thunder on but it will never be quite the same."
Weston has replaced former Greenhouse and La Trompette head chef Anthony Boyd who has left the company.