The mortgage, called First Active, is being positioned as a straightforward, standalone mortgage product.
First Active will complement the financial service's One Account, which is marketed as a lifestyle current account and targeted at young professionals.
It offsets mortgage payments against the balance of customers' current accounts.
First Active is set to launch in the autumn. The launch is being overseen by Jane-Anne Gadhia, the One Account's managing director.
David Ramsbottom, the One Account's marketing director, is responsible for building the marketing team for First Active.
The win strengthens Clemmow Hornby Inge's two-year relationship with the financial services provider.
The agency first won a place on its roster in November 2002 when it beat St Luke's, Partners BDDH and the incumbent, Wieden & Kennedy London, to its Advanta credit card account, which was later rebranded as the Mint Card.
In September last year, the agency added the £10 million business for the One Account, which RBS acquired from Virgin in 2001.
The One Account brief was originally held by TBWA\London, where the CHI partners Simon Clemmow and Johnny Hornby previously worked on the business.
The Royal Bank of Scotland's roster also comprises M&C Saatchi, which handles the advertising for NatWest.