Lord Armstrong of Ilminster told the BBC he "never felt a whiff of sexuality about Ted Heath, whether it was in relation to women, men or children".
Police are investigating historical child sexual abuse claims against Sir Edward who died in 2005 aged 89.
The Sir Edward Heath Charitable Foundation has said it is confident he would be cleared of any wrongdoing.
Lord Armstrong was principle private secretary at Number 10 during Sir Edward's time as Conservative prime minister between 1970 and 1974.
He said the allegations were "so totally uncharacteristic and unlikely" that he did not believe them to be true.
"My incredulity is based on the way of life of a man and about his character and his personality," he told Radio 4's Today Programme.
"When he was at home he had two policemen on the gate, he had the personal protection officer from Scotland Yard in the house, he never drove a car himself, he always had an official driver.
"It just seems to me highly unlikely that he could have escaped all that to do the kind of thing that is described."
He added: "I knew him for 35 years, I worked very closely with him while he was prime minister, and we remained friends for the rest of his life.
"You usually detect some sense of sexuality when you are friends or work closely with them. I think he was completely asexual. There are some people like that and I think he was one of them."
Historical child abuse: Key investigations
At least seven police forces are carrying out investigations linked to abuse claims involving Sir Edward.
Operation Hydrant, a national operation co-ordinating inquiries into historical abuse, has been liaising with forces which received information concerning him.
The Independent Police Complaints Commission said it would look at whether officers at Wiltshire Police failed to pursue allegations made against him.
A retired detective has alleged that claims were made in the 1990s but not followed up.
Sir Edward lived in Salisbury, Wiltshire, for many years and died at his home there.
Former Prime Minister Sir Edward Heath was "completely asexual", one of his closest advisers has said.