The case attracted international attention as the search for the blue-eyed little girl became desperate, eventually evolving into a potential murder case.
Portuguese police insist Kate and Gerry McCann remain suspects.
But Edgar dismisses the allegations detailed in a book published by Portuguese detective Goncalo Amaral, Madeleine: The Truth of the Lie.
"I was looking at everything and that would include them," he says. "If I found any evidence against Kate and Gerry I would have given it to the police immediately. Kate and Gerry would expect no less. But I found no shred of evidence."
Edgar had been hired by the Find Madeleine Fund with a small team of investigators to examine two key suspects.
There was little to implicate either of them, convicted paedophile Raymond Hewlett or local criminal Euclides Monteiro, he says.
Edgar handed over his files to police in 2011 when his investigation came to an end.
But he says he's kept close tabs on developments ever since.
'SOMEBODY KNOWS'
Now he says he is convinced it was a carefully planned kidnapping. But he isn't sure if it was conducted by an individual, or a gang.
"There was a very narrow window of opportunity for them to get away with Madeleine," he says. "So it does point to it being planned and some level of surveillance, perhaps of the apartment.
"If the motive was gang-related child prostitution, there might have been more than one involved."
This is why he believes a breakthrough is inevitable.
"They can't keep it to themselves and research has shown they always confide in someone else.
"I think that someone else apart from the perpetrator knows and that is one of the best hopes of getting to the truth, that someone comes forward and says what they know."
The attacker, he says, will have offended again.
"It's the type of crime they cannot help themselves, certainly if it was sexually motivated," he says.
It's not the first time Edgar has presented his sexual abduction theory. In 2009 he said Madeleine had likely been imprisoned in an underground dungeon.
He presented no evidence to support his claim.
Formal British police investigations are expected to wind-up later this year.