The move means fans of some of the BBC’s biggest shows – including TopGear and Doctor Who as well archive shows – will be able to buy episodes direct from the BBC.
BBC Worldwide’s DVD label already includes free digital copies in some of its DVD and Blu-ray titles, including last year’s Doctor Who 50th anniversary special.
BBC Store will be separate from the broadcaster’s popular iPlayer service which is funded by the licence fee and which will remain a free to use catch-up service.
Plans for the new service, which will see the BBC follow BT and take on Apple’s iTunes store, were announced by BBC Director-General Tony Hall in October.
Purchased shows are likely to be watchable on PCs, Macs and Tablets and could also be accessible on Smart TVs.
The Trust approved the store after assessing its impact on commercial rivals and the potential for reputational damage.
Suzanna Taverne, lead trustee on the assessment, said: “The BBC needs to respond to significant changes in the way audiences now buy programmes. The creation of BBC Store will enable it to do so, and to release a greater selection of classic shows from the BBC archive.
“In considering BBC Store, the Trust conducted a robust assessment and sought the advice of external parties. It concluded that BBC Store is a worthwhile commercial service that supplements what the BBC makes available through the licence fee and promises to bring value not only to audiences but also to the wider creative industries.”