Detectives released the new "age progression" image of the missing girl, which they said showed what she would look like today at the age of nine.
They said the image, created ahead of what would have been her ninth birthday on May 12, had been created in "close collaboration with the family".
Britain's biggest police force said that as a result of evidence uncovered during a review "they now believe there is a possibility Madeleine is still alive".
Detective Chief Inspector Andy Redwood told the BBC's Panorama programme that they have the "best opportunity" yet to find Madeleine, who went missing five years ago this week when she was three years old.
The officer said his team were "seeking to bring closure to the case" and that solving it was the "ultimate objective".
DCI Redwood is leading a team of 28 detectives and seven civilian support staff to comb through 40,000 pieces of information, including reports and documents from UK police, Portuguese police and private detectives hired by the McCanns.
He said one major advantage for Operation Grange is that for the first time it has access to all of the available evidence all in one place.
"At no time before have those three elements been drawn together in one place. And so what we've done over the past number of months is to bring to one place all those pieces of the jigsaw," he said.
Portuguese public opinion has been hostile towards Madelaine's parents, Kate and Gerry, but DCI Redwood said he is finding no antagonism from the Portuguese review team.
"Those officers are engaged, they are open, they are working with us collaboratively and I've not encountered with them any of those views," he said.
• BBC Panorama - Madeleine: The Last Hope? will be shown tonight, Wednesday 25th April, at 7.30pm on BBC One.