Kevin Halligen, 56, was found unwell at his girlfriend’s Surrey home and later died.
Police are treating his death as “unexplained” and are expected to pass a report to a coroner.
Mr Halligen’s company, Oakley International, was hired on a £500,000 contract by Kate and Gerry McCann and the administrators of the Find Madeleine Fund in 2008, a year after their daughter vanished in Portugal.
The McCanns had become frustrated with the failure of the Portuguese police to find Madeleine or any clue to what happened to her.
Mr Halligen portrayed himself as a James Bond-type figure, though a source said he was later considered “a bit of a fantasist”.
The McCanns ended the investigator’s contract in 2009, believing he had failed to deliver the work they were paying him for.
Dublin-born Mr Halligen, who had dual American and Irish nationality, was later extradited to the US where he admitted fraud charges over a previous contract.
He was jailed, but freed because of the time he had already served in custody and later returned to the UK.
In a TV interview he denied he had misused funds in his Madeline investigation and dismissed accusations of leading a lavish lifestyle.
Surrey Police said: “We were called to an address in Cobbett Hill Road, Normandy, Guildford, on Monday following a report of a man in his 50s having been taken unwell, who subsequently died.
“The death is being treated as unexplained and a file will be passed to the coroner’s office in due course.”
The McCanns did not comment, but it is understood they had had no association with him since terminating his contract.
Madeleine was nearly four when she disappeared from the family’s rented holiday apartment in Praia da Luz on the Algarve coast in May 2007.
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Her parents hired a series of private investigators who failed to find any trace of her.
In 2011 Scotland Yard began a new investigation, funded by the UK government, but has not solved the mystery – though its work continues.