Luchford APM had held the account for the previous five years.
Grosvenor head of media relations Naomi Curtis said that Luchford had "done a fantastic job", and was shortlisted for the new brief.
Mission is tasked with supporting the company's strategy to promote its London estate as a "great place to live, work and visit".
"A big part of the role will be to create integrated campaigns across experiential, digital and print to promote our retail streets, which include Mount Street, Duke Street, Pimlico Road, Motcomb Street and Elizabeth Street," Curtis said, adding that the agency would also support community and cultural events for locals and visitors.
Mission director Will Woodhams, who will lead the account alongside Mission campaign director Daisy Bell, said: "As the London Estate focuses on its retail portfolio we look forward to telling the amazing stories of both the estate and the world-class retailers."
The Grosvenor Group, which manages the Grosvenor family's estate, had £5.7bn worth of assets under management in the UK and Ireland as of the end of 2015.
The Mayfair and Belgravia estates came into the Grosvenor family in 1677, when it was a mixture of swamp, pasture and orchards. The group also owns other London properites and developments across the UK.
The 6th Duke of Westminster, the head of the family, died in August, passing the title to his son.