Rapp London already holds the digital and CRM Viagra account in the UK and Europe.
Pfizer recently awarded its US creative account to McGarryBowen. A spokeswoman for Pfizer told a : "Between McGarryBowen and Rapp all of the agency needs for Viagra are going to be met."
Over $120m was spent by Pfizer on marketing Viagra in 2008, according to TNS Media Intelligence.
The US is the world's largest pharmaceutical market and is home to most of the world's major manufacturers, such as Pfizer, Merck & Co and Bristol-Myers Squibb.
The largest is Pfizer, with worldwide pharmaceutical revenues in 2007 of US$44.4 billion. The US market is understood to account for half of this.
UK rules for marketing of prescription drugs differ from the US, in that direct promotion of prescription drug brands is not allowed. In the UK Rapp promotes the health issues around erectile dysfunction, rather than the brand itself.