The win follows a four-way pitch involving incumbent agencies Walker Media and ZenithOptimedia, and a final shoot-out with Carat.
The business was previously divided between Walker Media, which managed the Quorn account, and ZenithOptimedia, which handled Premier Foods' brands Ambrosia and Branston Pickle, as well as the Campbell's range.
Starcom UK chief executive Linda Smith said: "It's been an interesting year. I am delighted for the whole team.
"It's been a company effort and that, combined with the open process of the pitch, has created a sense of excitement and momentum for Starcom."
Premier Foods purchased the Campbell Soup Company, including brands such as Oxo and Batchelors, in July for £460m.
Quorn became part of Premier Foods in 2005 after Marlow Foods was acquired for £172m.
The merged company will have annual sales of £2.6bn, with 93% of revenues coming from the UK.
RHM's culinary, cake and bakery divisions manufacture some of the nation's most iconic brands, such as Bisto, Sharwood's sauces, Robertson's jam, Mr Kipling, Hovis and Mothers Pride.