The publicist was held at his Surrey home at 7.40am on suspicion of sexual offences and taken to Belgravia police station in central London for questioning.
He was arrested as part of Operation Yewtree, the investigation into allegations of sexual offences surrounding Savile and others, before being released at around 9.20pm on Thursday.
Speaking outside the police station, a shocked-looking Clifford said: “These allegations are damaging and totally untrue.
“On a personal level, they are very distressing for myself, my wife, my family and loved ones.
“Anyone who really knew me all those years ago and those who have known me since will have no doubt that I would never act in the way that I have today been accused.”
He added that the allegations related to events in 1977.
Operation Yewtree, the investigation triggered by allegations against Savile, divides those arrested into three categories – allegations against Savile himself, allegations against Savile with others, and allegations against others on their own.
Mr Clifford has been classified as “others on their own” and there is no suggestion that he had any links to Jimmy Savile.
He is the latest in a string of high-profile names who have been arrested as a part of Operation Yewtree. Others arrested include radio presenter Dave Lee Travis, comedian Freddie Starr and disgraced pop star Gary Glitter.