The 77-year-old singer was awarded £210,000 damages in the landmark privacy case, as well as an additional £850,000 in costs.
The BBC had attempted to overturn the original ruling, saying there was a “compelling reason” for an appeal.
Lawyers for the broadcaster cited “a severe chilling effect” on press freedoms.
Sir Cliff sued the broadcaster following its coverage of a South Yorkshire Police raid on his home in Sunningdale, Berkshire, in August 2014.
Officers were investigating an allegation of historic child sex abuse against him, which the star has always denied.
He was never arrested or charged with any offence.
In his original ruling, High Court judge Mr Justice Mann said the BBC had infringed the celebrity’s privacy rights in a “serious and sensationalist way”.
Mr Justice Mann awarded £190,000 in general damages to cover “the general effect on Sir Cliff and his life”, plus an additional £20,000 in aggravated damages, due to the fact the BBC later submitted the story for an award.
The £850,000 in costs must be paid by the BBC within 14 days.
Barrister Gavin Millar QC, who leads the BBC legal team, described the damages award as “wrong in law” and said there would be widespread implications for journalists reporting police investigations.
Sir Cliff’s lead lawyer, Barrister Justin Rushbrooke QC, said the judge had applied “law to the facts” and said it was “about time the BBC took a realistic view of this matter”.
The BBC is now left with one further option – to seek permission to appeal at the Court of Appeal.
The broadcaster has not yet said whether it will do so.
Sir Cliff – who said he was left in “creative limbo” for two years following the raid – is understood to no longer be seeking indemnity (such as loss of earnings) from the BBC.
The star has previously said the case cost him £3.4m.
South Yorkshire Police previously settled a damages claim with Sir Cliff out of court, agreeing to pay him £400,000.