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".

The ancient creature has been preserved in exquisite detail, providing the oldest-known record of hedgehog-like spines and mammalian internal organs.
The discovery is published in the journal Nature.
The creature, called Spinolestes xenarthrosus, was unearthed in Las Hoyas Quarry in central Spain.
Study co-author Dr Zhe-Xi Luo, from the University of Chicago, US, said: "Spinolestes is a spectacular find.
"It is stunning to see almost perfectly preserved skin and hair structures fossilized in microscopic detail in such an old fossil.
"This Cretaceous furball displays the entire structural diversity of modern mammalian skin and hairs."
The specimen's liver, lung and diaphragm tissues were found intact, as well as fur, spines and scales.
"Normally you find bones and you find skeletons - and there are many, many fossil mammal skeletons found, but never these soft parts in such great detail," explained Prof Thomas Martin, from the University of Bonn, Germany.
The creature was small, somewhere between the size of a mouse and a rat, weighing about 50-70g.
It had big ears and a pointy face, with a short mane and a soft fuzzy belly. It was most likely ground dwelling and ate insects.
"It is cute, very cute," said Prof Martin.  "It looked like a modern spiny mouse, which is also quite cute."
But in addition to its adorable attributes, Spinolestes also had a defensive side.
It had small spiky spines on its lower back, as well as scales similar to an armadillo's, helping it to fend of predators.
"If a predator comes and bites it on the back, then the spines are easily shed and the predator is left behind with a mouth full of spines, so it can escape" said Prof Martin.
Potential predators probably included small dinosaurs, which have also been unearthed from the same site in Spain.
Crocodiles, salamanders, frogs, birds and insects have also been found there.
And while central Spain is hot and dry today, 125 million years ago it would have been a lush tropical wetland.
"These animals lived in a swampy environment comparable to the modern Everglade system," added Prof Martin.
The creature was discovered by a team led by Angela Buscalioni from the Autonomous University of Madrid, in Spain.
Follow Rebecca on Twitter
Sir Cliff Richard and South Yorkshire Police have settled a legal fight over reports naming him as a suspected sex offender.
[NEXT_CONCEPT]
A 125 million-year-old fossil - described by scientists as an exceptionally cute furball - has been unearthed, scientists report.