The deal concludes protracted talks which started in late 2008 and involved a lengthy court battle over a licensing agreement for the business.
2etertain launched in 2004 as a 60:40 joint venture between Worldwide and Woolworths for the publishing and distribution of BBC DVDs around the world.
Following the collapse of Woolworths in 2008, Worldwide asked the retail chain's administrator Deloitte about purchasing the remaining 40% stake in 2entertain.
Worldwide was initially prepared to pay around £110m to secure the stake, but subsequently argued that the licensing agreement allowing 2entertain to publish DVDs containing BBC programming expired when Woolworths went into administration. This would, therefore, make the retailer's 40% stake virtually worthless to anyone but Worldwide.
Last August, a judge ruled in favour of Worldwide in its case against Deloitte, a verdict which was reinforced by an appeal court in November.
Worldwide has now agreed to pay £17m for the 40% stake, with funding coming from existing cash in the business without the need for licence fee support.
"I am pleased that we have finally concluded these negotiations, and have secured the future of 2entertain," said BBC Worldwide chief executive John Smith.
"This comes as good news for a variety of stakeholders. 2entertain's retail partners know it is now backed by a stable owner. Consumers can continue to enjoy BBC content on DVD in their own homes.
"The independent production sector already works closely with 2entertain. And licence fee payers will continue to benefit from 2entertain's contribution to BBC Worldwide, which helped us return a total of £153m to the BBC in the last financial year."
Paul Dempsey, chief executive of 2entertain and managing director of BBC Worldwide home entertainment, added: "The 2entertain business has not been distracted by the events of the past 18 months, continuing to deliver impressive results.
"Under full BBC Worldwide ownership, it now looks forward to a more settled period and playing an important role in BBC Worldwide's future plans."