The deal, which comprises more than 30 magazines, is expected to be ratified by the Office of Fair Trading in the autumn whereupon staff will transfer to a new company set up by Exponent.
The arrangement includes the outright sale of magazines "less closely aligned" to BBC programming, such as Olive and Gardens Illustrated, as well as Radio Times.
However BBC and BBC programme branded titles such as Gardeners' World will be licensed under terms that, while ownership will transfer to Exponent, some editorial control will be retained by BBC Worldwide division BBC Magazines.
For key BBC brands, such as the magazines for Top Gear as well as Lonely Planet and Good Food, the new Exponent-owned business will act as a contract publisher.
The acquisition includes BBC Magazines' interest in subscriptions fulfilment business Dovetail - a joint venture with Dennis Publishing - as well as its share in distribution company Frontline. Additionally Exponent will acquire Origin Publishing in which the BBC has a minority share.
BBC will sell its stake in Indian publishing company Worldwide Media to fellow shareholder Bennett, Coleman & Co.
The deal is expected to raise £121m, most of which is expected to go to the BBC.
BBC staff were informed of the sale earlier today in an email from BBC Worldwide chief executive John Smith who said: "I believe that the deal with Exponent offers the best prospects for BBC Magazines to continue on the path of success. This transaction brings a focus and degree of investment that BBC Worldwide alone is unable to provide. We believe this will put BBC Magazines in the strongest position to meet the challenges and opportunities that lie ahead in a rapidly evolving market."
Richard Lenane of Exponent, said: "We are delighted to have signed an agreement with BBC Worldwide for its magazines business, pending OFT approval. Exponent invests exclusively in market-leading businesses which have strong growth potential and great people.
"We look forward to working with the BBC Magazines team and in partnership with BBC Worldwide to continue to develop the BBC magazine franchise and to take advantage of the growth opportunities afforded to the business outside BBC Worldwide ownership."
Exponent was unavailable for further comment.
In a statement, BBC Worldwide said the deal had the full approval of the BBC Trust and will create a business unit to oversee the management, editorial compliance and contractual relationship under the agreement.
BBC Magazines made a profit of £21.6m, up 9.1% year-on-year, on revenues of £164.5m, down half a percent, in 2010.
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