POLICE: Absconded prisoner from Doncaster still on the runSir Cliff was also named despite never being arrested or charged over the allegation.
In 2016 the BBC said it was "very sorry" that Sir Cliff Richard "suffered distress" after its coverage, but defended its decision to report the investigation.
Mr Justice Mann oversaw a trial at the High Court in London during April and May and is scheduled to deliver a ruling on Wednesday.
The BBC has to pay 65 per cent of the $336,000 while South Yorkshire Police, who conducted the raid, will pay 35 per cent.
The BBC disputed his claims and senior editors said the coverage was accurate and in good faith.
"I'm choked up, I can't believe it, it's wonderful news", Sir Cliff told reporters outside the court.
The judge ruled that Richard's privacy rights were infringed in a "serious" and "somewhat sensationalist" way.
The 77-year-old singer took legal action against BBC bosses over broadcasts of a South Yorkshire Police raid on his home in Sunningdale, Berkshire, in August 2014, following a child sex assault allegation.
Alleged incident Billy Graham at Sheffield United’s Bramall Lane ground in 1985
Prosecutors later said Richard, who maintained his innocence throughout, would face no charges due to lack of evidence.
He thundered: "The BBC should never have spent license fee payers' money onthis, they should have issued a full and fulsome apology to Sir Cliff Richard at the beginning".
BBC director of editorial policy and standards David Jordan said resignations were "not necessarily the right response to every mistake that every journalist makes in a news organisation".
This was based on the fact that he did not believe the police volunteered information about the raid to the BBC, but that the police were "manoeuvered into providing it from a fear and implicit threat that the BBC would or might publish news of the investigation before the police were ready to conduct their search".
"I think that they, or majority, were far more impressed by the size of the story and that they had the opportunity to scoop their rivals".
He said the BBC refused to apologise and insisted it had run a public interest story.
"In many situations, the publishing of the name of someone under investigation has led to other witnesses and victims coming forward".
She added: "The media is going to have to walk on eggshells when reporting on police investigations from now on".