The six-year deal, which begins on 10 May, will see Peyton and Byrne run two self-service cafes, a family restaurant and creamery and a waiter-service restaurant within Kew's Orangery. All four venues will be refurbished during the first year of the contract.
Peyton will oversee a change in menus from choices such as burger and chips to fillet of halibut en papillotte with fennel, black pepper and borage flowers (£14).
Peyton, who is chairman of Peyton and Byrne, said he lived near Kew and was aware of the shortcomings of its catering. "It's our largest project - there's an awful lot of covers. We want to increase turnover substantially. My job is to come along, look at it and see how we can make it different. We can really can make a difference.
"There's a lot of knowledge at Kew. We're looking for them to come up with relationships throughout the world to bring food to the public using their knowledge."
RBG Kew's head of commercial activities Joni Marks said Kew's visitors, who numbered 1.3m last year, needed catering that complemented the garden experience: "We had burger and chips before. The food was contradicting the experience. People expect to see food aligned to gardens. Peyton showed what he can do at the National Gallery, Wallace Collection and British Library."
Marks said people can expect to see Kew-branded coffee and cocoa in multiple retailers soon. He added: "We're working with the innovation unit at Kew to develop our own coffee brand, roasting our own coffee on site.
"This is a big contract with vast potential. We're putting in significant capital investment. Peyton and Byrne will develop each facility to improve and differentiate the offer so it is aligned to the garden. Visitors come for three-and-a-half or four hours on average and catering is integral to people's visits. People go to eat as well as view."
Peyton will develop and market a Kew catering garden brand. Marks said: "We have four restaurants that are all quite similar at the moment. We will differentiate them - for instance, the Orangery will revert to being an orangery. The horticulture team is developing a plant display inside and linking plants to food on the plate.
Peyton runs restaurants within famous London landmarks including Inn the Park in St James's Royal Park, the National Dining Rooms and National Cafe at the National Gallery, the Wallace Collection, Meals at Heal's and the Institute of Contemporary Arts Bar & Cafe.
In addition Peyton and Byrne also has cafe/bakery outlets at Heal's, the British Library, St Pancras International railway station and the Wellcome Collection.