The agency, which launched in January this year with backing from Vallance Carruthers Coleman Priest, triumphed in a five-way battle for the business.
The losing shops were Craik Jones Watson Mitchell Voelkel, Toast, Tullo Marshall Warren and Barraclough Edwards Chamberlain.
The agency replaces a roster of agencies that included WWAV Rapp Collins and Hawkins Direct. The brief covers acquisition and customer marketing.
More Th>n is the first client Stephens Francis Whitson has won independently of VCCP. The agency launched with the clients Dyson and Disney, which it shares with VCCP.
The pitch was overseen by Neil Scaise, More Th>n's head of marketing and communications, who said: "Our real need is for a strategic partnership. We spend a lot of money on this kind of work."
Chris Whitson, the planning partner at Stephens Francis Whitson, said: "More Th>n really does have a point of difference and we are excited."
The brand's advertising, which features Lucky the dog, remains with CCHM:Ping.