Speaking out as police searched his apartment in Berkshire, the star said: "For many months I have been aware of allegations against me of historic impropriety which have been circulating online.
"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 cooperate 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."
Sir Cliff, who is rumoured to be in Portugal, issued a statement via his representatives after widespread media coverage of the search of his home.
South Yorkshire Police confirmed officers entered the property today in relation to the alleged sexual assault of a boy under 16 in the 1980s and that nobody had been arrested.
It is understood that the singer's lawyers have been in contact with the force.
The search is not connected to Scotland Yard's Operation Yewtree, launched in the wake of the Jimmy Savile scandal.
A South Yorkshire Police spokeswoman said: "South Yorkshire Police has gained entry to a property in the Sunningdale area of Berkshire.
"Officers are currently searching the property.
"A search warrant was granted after police received an allegation of a sexual nature dating back to the 1980s involving a boy who was under the age of 16 at the time.
"No one has been arrested and the owner of the property was not present."
Thames Valley Police confirmed that it had helped the South Yorkshire force with the execution of the search warrant.
Born as Harry Webb in Lucknow, India in 1940, Sir Cliff has become one of the most enduring stars of his time, with hits including Devil Woman and Living Doll.
He was knighted in 1995, the first rock star to be so honoured and performed at the Queen's Diamond Jubilee concert at Buckingham Palace in 2012.
A handful of television crews, reporters and photographers were gathered near the gates to the private estate in Sunningdale, which includes a grade II-listed mansion, manicured lawns and acres of land.
Cars could be seen going in and out of the brown gates to the long driveway up to the property, although no uniformed police officers were standing guard.
The art deco estate, which also features a spa, a 50ft swimming pool, a tennis court and a water feature, was built in the 1930s.