Bradley-Jones, previously executive vice-president, digital media and business development at BBC Worldwide in New York, will replace Kym Niblock, who is leaving for a role with a new company.
BBC Worldwide would not reveal details of her new appointment.
He will be responsible for the strategic direction and management of the BBC.com business.
The site had 50 million unique users between January and March 2009, according to Omniture.
BBC.com will also be looking to roll out the iPlayer internationally within the next 18 months, once content rights issues are resolved.
Some content could be available on a paid-for basis.