Keown, who was also a finalist in the 2015 UK San Pellegrino Young Chef of the Year competition, said he was hoping to make his mark on the historic restaurant.
"I'm excited about this new challenge...the food I cook focuses on twists on British classics, using great produce, sourced from interesting producers," said Keown,
"I am hoping to rejuvenate the restaurant, working closely with the team and within the ethos of Tate Britain to deliver great food."
He joins the Tate after a seven-year stint at The Bell Inn in Hordon-on-the-Hill, named one of the top ten pubs of 2017 in this year’s Good Pub Guide.
The Rex Whistler has also announced the appointment of Matthew Randall as its new restaurant manager.
Randall has worked across the world at venues including The H Hotel in Dubai and with Fairmont Hotels in London, Scotland and Canada.
He said he was aiming to develop the restaurant’s existing reputation.
“I am looking forward to working with Garrett and the Tate Britain team to deliver exceptional food and drink alongside events at the Rex Whistler and across Tate Britain,” said Randall.
The Rex Whistler first opened in 1927 and features a famous mural, The Expedition in Pursuit of Rare Meats, painted by the 23-year-old artist who lends his name to the restaurant.
Keown will present his first menu at The Rex Whistler on 5 October.