A controversial investigation by Wiltshire Police found that there would be evidence to question the senior Tory over claims he raped an 11-year-old and assaulted several other children if he were still alive now.
The £1.5 million ($2 million, 1.7 million euro) probe was triggered in 2015 after Heath was named as a suspect in an investigation into so-called historical child sex abuse. None of these concern the period during which Heath was prime minister.
The Independent Inquiry into Child Sexual Abuse (IICSA) has said it would investigate further.
Each allegation was investigated, and in 24 cases the police took a direct statement from the alleged victim.
She branded the inquiry "a disgrace" and said one of Heath's key accusers had made "pernicious" claims of satanic ritual abuse and said she was "profoundly disturbed" by uncorroborated witnesses.
An alleged rape and indecently assault on an 11 year old boy during a paid sexual encounter in a home in London in 1961.
Claim: Heath allegedly indecently assaulted a 15-year-old boy during a chance encounter in a public building. In total the alleged incidents span 31 years, from 1956 to 1992.
"All those who knew Sir Edward Heath or worked with him are, without exception, convinced that the allegations of child abuse will all be found to be groundless", they added.
Sir Edward Garnier said the conclusions related to seven outstanding matters were an attempt to justify the police inquiry.
Sir Edward was born in Kent in 1916 and studied at Balliol College Oxford, becoming president of the Oxford Union.
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The investigation began in August 2015, after the police complaints commission announced it was investigating how Wiltshire Police had dealt with a court case relating to Edward Heath in 1994.
Former British Prime Minister Edward Heath and West German opera singer Anneliese Rothenberger pose sitting at a piano during an interval in shooting for a Television show in Hamburg, West Germany on May 17, 1977. He was one of the people who was around in our lives. The claims made covered 14 different police force areas in the United Kingdom and the Channel Islands and covered a period from 1956 to 1992.
Three further claims would not have merited an interview because those who made them later told police they were "genuinely mistaken in naming" Heath as the perpetrator.
'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.
However police stressed that no inference of guilt should be drawn from the inquiry's conclusions. Presumption of innocence was enshrined in the law, Veale said.
Heath's reputation should not be left in limbo, his former colleagues 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.
He said the investigation had been conducted objectively, with respect and without fear or favour.
In it, he said the decision to undertake the "incredibly complex and challenging investigation" was "not taken lightly", but added he would not be "buckling under pressure not to investigate or to conclude the investigation prematurely".