The announcement follows a competitive tender process started in 2010 and the decision to move into exclusive talks with Exponent has been approved by the BBC Trust.
Discussions will continue with Exponent, with a view to completing an agreement this summer, subject to the final approval of the BBC Trust.
Exponent, which owns thetrainline.com and Gorkana, first emerged as a rival to magazine publishing companies last month.
Any deal is expected to involve all the titles of BBC Magazines' core portfolio, as stated by BBC Worldwide from the outset, although any individual licensing conditions are yet to be confirmed.
The official announcement will be welcomed by staff at BBC Magazines, who have had to endure months of speculation regarding their future.
The foundation for any BBC Magazines deal was formed back in March 2010, when in the run-up to the general election, and after months of pressure, BBC director general Mark Thompson suggested change was coming to the division.
He said: "In the future, Worldwide will focus in particular on international, as opposed to UK, business development, on evolution rather than merger and acquisition, and over time will move away from exploitation in physical media like magazines."
This was followed a month later with BBC Worldwide confirming it hopes to hold preliminary conversations with interested companies, but stress any deal was dependent only finding an "appropriate partner who understands the BBC’s values and brands".
BBC Magazines publishes many of the UK's most popular lifestyle, factual and children's titles, including Radio Times, Good Food, Gardeners' World, Top Gear, BBC History Magazine, CBeebies Weekly and Doctor Who Adventures.