The initial service will offer downloads of BBC programs for up to seven days after broadcast. The shows can be viewed for up to 30 days after download.
In addition, 15 percent of content will be "series stacked," in which selected series can be played in their entirety for 30 days following transmission of the final episode.
The approval further boosts the corporation's efforts to embrace the Internet and follows the recent content deal with YouTube and
A BBC spokeswoman said: "It's another platform for our audiences to get hold of BBC content."
The BBC's independent governing body, the BBC Trust gave the final go ahead on Monday following a "public value test" that garnered responses from around 10,500 individuals and organizations.
Diane Coyle, BBC Trustee and chair of the Trust's PVT steering group, said the consultation demonstrated considerable public support for iPlayer.
Ashley Highfield, the BBC's director of future media and technology, said the iPlayer is a critical part of the strategy to "maintain impact and relevance in a world where viewing and listening habits are shifting from linear to on-demand."
Mark Thompson, the BBC's director general, said he is delighted with the trust's decision to approve the proposals.
He added it is significant as these on-demand proposals are "at the heart" of the BBC's creative future. The launch date for the iPlayer service will be announced in the future.
Tim Ferguson of Silicon.com reported from London.