A lawyer representing Sir Cliff gave Mr Justice Mann the news at a High Court hearing in London on Thursday.
Barrister Justin Rushbrooke QC did not give an overall figure but said BBC bosses had agreed to pay £850,000 on account.
Sir Cliff told the trial he had spent more than £3 million on the case.
Barrister Gavin Millar QC, who leads the BBC legal team, said it was “appropriate” for the BBC to pay legal costs incurred by Sir Cliff relating to issues determined as a result of a trial earlier this year.
The 77-year-old singer sued over BBC coverage of a South Yorkshire Police raid on his home in Sunningdale, Berkshire, in August 2014, following a child sex assault allegation.
Earlier this month Mr Justice Mann ruled in Sir Cliff’s favour following a trial in London.
The judge concluded that coverage was a “very serious” privacy invasion and awarded Sir Cliff £210,000 damages.