A Wiltshire Police investigation codenamed Operation Conifer concluded that seven of the claims would have been sufficiently credible to justify questioning Mr Heath, who was prime minister between 1970 and 1974, under caution.
Police inquiries into allegations against him cost £1.5 million.
Mr Heath, who had been MP for Bexley, died at his home in Salisbury in July 2005, aged 89.
His friends have sought to discredit the police investigation, calling it “profoundly unsatisfactory” and complaining that it had left a “cloud of suspicion” hanging over him.
However, Wiltshire Chief Constable Mike Veale strongly defended the decision to launch Operation Conifer.
“There have been many views expressed as to whether the police should investigate alleged offences committed by a deceased suspect,” he said.
“I believe this was the right moral, ethical and professional thing to do, but I appreciate that every case needs to be judged on its own merits.
“Sir Edward Heath was an extremely prominent, influential and high-profile person who was arguably one of the most powerful people in the world commensurate with the political office he held.
“The allegations against him were of the utmost seriousness and from a significant number of people.
“I hope people will understand that, given these circumstances, it would be an indefensible dereliction of my public duty as a chief constable not to have investigated such serious allegations against a former prime minister, even though he is deceased.
“I recognise that this investigation, the findings and the summary closure report may raise further questions.
“But I also believe it signals a watershed moment for people and victims who have suggested or implied there has been a state cover-up for some senior figures who may have been involved in child sexual abuse.
“There’s been a huge and significant amount of speculation and misleading commentary in the public domain but specifically there has been no political pressure whatsoever in relation to the conduct and delivery of the outcomes of this investigation,” Mr Veale said.