The singer sought damages from the force, and the BBC, over media coverage of a police raid on his home in 2014.
On Friday, lawyers told High Court judge Mr Justice Mann that Sir Cliff and the force had come to terms.
The BBC, which is still disputing the claim for damages, said it "had a duty to report" the investigation.
Sir Cliff said live BBC coverage of the police search of his home in Sunningdale, Berkshire, invaded his privacy.
He sought "very substantial" compensation from both South Yorkshire Police and the BBC.
In a statement on Friday, a BBC spokesman said: "The BBC's responsibility is to report news stories that are in the public interest."
The corporation said the "extensive disclosure of historical child sexual abuse" by other celebrities made the investigation - and a subsequent police decision to search his home - a worthy news story.
"A search happened, and because it did, the BBC reported it - just as any other media organisation would have and did," the spokesman said.
South Yorkshire Police had already apologised "wholeheartedly for the additional anxiety caused".
The force learned of the sex offence allegations in July 2014, searching Sir Cliff's Berkshire flat the following month.
In June 2016, the Crown Prosecution Service announced Sir Cliff would face no charges.
The star's lawyers said he suffered "profound and long-lasting" damage from coverage of the search, and from being publicly named as a suspected sex offender.
They also say South Yorkshire Police contravened guidance on "relationships with the media".
Sir Cliff Richard and South Yorkshire Police have settled a legal fight over reports naming him as a suspected sex offender.