The media regulator said the BBC was guilty of a "serious and repeated" failure to adhere to broadcast regulations after the word "fuck" was used on six different occasions by singers including Madonna, Phil Collins and Johnny Borrell.
Madonna told the audience at one stage during the concert: "Come on, motherfuckers! Jump!"
The swearing drew 22 complaints to Ofcom and around 150 to the BBC.
Ofcom said it had already warned the BBC about offensive language after it was used during coverage of the Live8 concert in 2005.
A summary of the regulator's findings will be aired on BBC One at 7pm on Saturday, April 12, and at 4pm on the same day on BBC Two.
The ruling marks the first time the BBC has been forced to make an on-air statement in a case relating to a breach of broadcast rules.
Ofcom said: "The evident failure of the BBC to have put in place adequate precautions to minimise the chances of the same thing happening again, resulted in the need to impose a statutory sanction.
"In the circumstances of this case the desire to broadcast the event 'live' did not outweigh the need to take appropriate measures before the watershed to protect viewers, and in particular children, from offensive language."