Ferguson has been facing escalating fines under new Premier League rules for his boycott on talking to the BBC, which dates back to an unflattering Panorama documentary in 2004 about his son Jason's dealings as a football agent.
However, the veteran Scot has decided to end the ban after holding peace talks with the BBC director general Mark Thompson and BBC North director Peter Salmon, in which the differences were "resolved to the satisfaction of both parties".
In a statement, a spokesperson for Manchester United said: "Sir Alex and the BBC have put behind them the difficulties which led to Sir Alex feeling unable to appear on BBC programmes.
"This follows a meeting between Sir Alex and the BBC's director general, Mark Thompson, and BBC North director Peter Salmon, and the issues have been resolved to the satisfaction of both parties.
"Sir Alex will now make himself available to the BBC for Match Of The Day, Radio 5 Live and other outlets as agreed. No further comment will be made by either party on this issue."
Manchester United's next match is on Sunday against Arsenal at Old Trafford.
In August last year, Match Of The Day host Gary Lineker called on Ferguson to end his boycott, saying that the Manchester United fans were the "ones missing out".
"It's a shame. We would like him to speak to us because we respect him and his teams, and always have done," said the former England striker at the time.
"It makes no difference to the programme because it's action-led. But it does make a difference to the Manchester United fans. They are the ones missing out.
"I get letters saying, 'We never hear from Sir Alex', and I have to explain. It's something he feels very strongly about, so what can you do?"
Last month, Glasgow Rangers manager Ally McCoist banned the BBC from interviews and press conferences after accusing the corporation of editing footage to suggest he was making light of football violence.