The 73-year-old singer said he had seen allegations that he abused a boy at a Billy Graham rally on the internet for months, but had chosen not to dignify them with a response.
After officers removed a number of items from the flat in Sunningdale, Berkshire, Sir Cliff, who is in Portugal, pledged to co-operate with the inquiry.
Eight officers removed a number of items from the property, which is situated in a gated development, before leaving in a fleet of unmarked vehicles.
The allegation involves a boy who was under the age of 16 in June 1985. The assault is alleged to have taken place at Sheffield United FC's Brammall Lane ground, when US evangelical preacher Mr Graham was staging a rally.
Sir Cliff's lawyers have been in contact with police. The inquiry, which is being co-ordinated by South Yorkshire Police, is not connected to Scotland Yard's Operation Yewtree probe, launched after the Jimmy Savile scandal.
The pop star, who has sold more than 21 million tracks in the UK, making him the country's third top selling singles artist, said: "The allegations are completely false. Up until now I have chosen not to dignify the false allegations with a response, as it would just give them more oxygen.
"However, the police attended my apartment in Berkshire today without notice, except it would appear to the press.
"I am not presently in the UK but it goes without saying that I will co-operate fully should the police wish to speak to me.
"Beyond stating that today's allegation is completely false it would not be appropriate to say anything further until the police investigation has concluded."
South Yorkshire's Detective Superintendent Matt Fenwick stressed the investigation was in its early stages. He confirmed officers had gone into the flat after a warrant was obtained following a historic sex allegation. He added: "No-one has been arrested at this stage and the owner of the property is not present."
Born Harry Webb in India, Sir Cliff, who started out with the Shadows, has had hits including Devil Woman and Living Doll. He was knighted in 1995 and performed at the Queen's Diamond Jubilee concert at Buckingham Palace in 2012.