The force called its investigation “impartial and thorough”, stressing its legal duty to look into criminal allegations made against deceased suspects.
During the investigation, three people were arrested on suspicion of non-recent child abuse, with two released without charge and the third still under investigation.
Lord Macdonald QC, the former Director of Public Prosecutions, accused Wiltshire Police of “covering their backs” at the expense of a man who can no longer defend himself.
Its findings will be passed to the wide-ranging Independent Inquiry into Child Sexual Abuse, which is being chaired by Professor Alexis Jay.
Wiltshire Police’s probe has proven controversial since a senior police officer made a television appeal outside Sir Edward's former home in Salisbury in August 2015, urging victims to come forward.
Chief Constable Mike Veale said there were “compelling and obvious reasons to investigate” the allegations.
“Sir Edward Heath was an extremely prominent, influential and high-profile person who was arguably one of the most powerful people in the world,” he added.
“No inference of guilt should be drawn by the decision to interview under caution,” a spokesperson said.
“The account from Sir Edward Heath would have been as important as other evidence gathered as part of the wider investigation.” They include the alleged rape of an 11-year-old boy, indecent assault of a 10-year-old boy and the indecent assault of a 15-year-old boy during three “paid sexual encounters”, and are said to have occurred between 19 in London, Kent, Sussex, the Channel Islands and Wiltshire.
The Conservative MP for North Wiltshire, James Gray, said Sir Edward “couldn’t possibly have done” what was claimed at times where he was under 24-hour close protection or taking thyroid medication that made him “sexually inactive”.
He added that he would be raising calls for a review in the House of Commons on Monday.
Of those, 19 were found not to meet the threshold for interview, three complaints were withdrawn, 10 were reported by a third party and another three allegations were made anonymously.