Until now, the broadcaster has been restricted to offering only limited amounts of long-form content available permanently online. Any significant expansion of the scope of audio and video archive availability online requires the approval of the BBC Trust.
Under the new plans, about 1,000 hours a year of long-form Radio 4 documentaries will be uploaded to bbc.co.uk/archive and made available to stream for an unlimited time.
The selected programmes will have an emphasis on factual content. They will include strands such as Desert Island Discs, Front Row and documentaries covering politics, business, law, finance, health, education, food and farming, international affairs, religion, ethics, travel and gardening.
BBC Four will publish about 150 hours of archive programming online each year, and Radio 3 will make about 420 hours available.
The BBC Trust said it believed the archive project fitted in with the corporation's editorial priority of "inspiring knowledge, music and culture".
The approval came as the Trust published its review into how Radio 3, Radio 4 and digital station Radio 7 are performing.
The review found that Radio 4 was serving audiences well, but the Trust was concerned that it was not doing enough to appeal to younger audiences who were interested in speech radio, as well as those living outside London and from black and minority ethnic backgrounds.
The Trust also approved the BBC's proposal to rebrand digital station Radio 7 as Radio 4 Extra.
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