The Met Police said it still believed there was a chance Madeleine was alive and it was investigating 38 "persons of interest" after reviewing the evidence.
Madeleine's parents, Gerry and Kate McCann, said the shift from review to investigation was "a big step forward".
Madeleine was almost four when she disappeared in Portugal in May 2007.
She went missing from her family's holiday flat in the Algarve resort of Praia da Luz, as her parents dined out with friends at a nearby restaurant.
Portuguese authorities dropped their investigation into her disappearance in 2008, but Scotland Yard started a review in May 2011, after Prime Minister David Cameron had responded to a plea from the McCanns, of Rothley, Leicestershire.
Det Ch Insp Andy Redwood, who is heading what has been called Operation Grange, said: "The review has given us new thinking, new theories, new evidence and new witnesses."
His 37-strong police team is two-thirds of the way through examining 30,500 documents from files held by the Portuguese, private investigators and British police. Some fresh interviews have also taken place.
"Over the last two years what the review has told me is that there is no clear, definitive proof that Madeleine McCann is dead," Det Ch Insp Redwood said.
"So on that basis, I still genuinely believe that there is a possibility that she is alive."
He added: "It is a positive step in our hunt for Madeleine that our understanding of the evidence has enabled us to shift from review to investigation."
Scotland Yard's decision to formally open its own investigation - which, like the review, will be funded by the Home Office - follows extensive discussions with UK prosecutors and the Portuguese.
BBC home affairs correspondent Danny Shaw said: "It's highly unusual - although not unprecedented - for a British police force to launch its own inquiry into an incident abroad."
In a statement, the McCanns said: "Kate and Gerry warmly welcome the shift in the Met's emphasis from review to investigation.
"It is clearly a big step forward in establishing what happened and, hopefully, towards bringing whoever is responsible for Madeleine's abduction to justice."
The Met said the 38 "persons of interest," who include 12 British nationals, are from five European countries - Portugal, the UK and three unnamed others.
Detectives say they need to find out more information and collect evidence on them and are not anticipating any immediate arrests.
The 12 UK nationals, who are not all currently in the UK, are believed to have been in Portugal at the time of Madeleine's disappearance.
The Met said it was "at an advanced stage of dialogue" with the other countries involved, and enquiries would be continuing with their assistance in the months ahead "to establish more information about the individuals concerned and any potential involvement".
A foreign national resident abroad could not be prosecuted in the UK for any possible crime that may be linked to Madeleine's disappearance.
Detectives say Madeleine's parents, the friends the McCanns were with in Portugal and people known to the family before they went away are not suspects or people they need to investigate.
The investigation is currently closed in Portugal and as part of the country's criminal justice system it cannot be reopened unless judges are convinced there are solid grounds to do so.
British police have formally asked the Crown Prosecution Service to submit an international letter of request to Portuguese authorities for assistance in obtaining evidence relating to their inquiries.
The Met has asked for a small number of its officers to be present in Portugal for the inquiries there.
As part of the review, a computer-generated image of how Madeleine might have looked at the age of nine was created with the help of her family. They marked her 10th birthday on 12 May.
By May 2012 - one year into the review - the Home Office's costs had reached £1.9m. The Met Police said a more up-to-date figure for the cost of the review would be released in due course.
The former head of the National Police Improvement Agency Peter Neyroud said it was a difficult investigation because it involved two countries, possibly more.
"It was always going to be an expensive inquiry and it is a fine judgement as to how far you go on but if, as appears, there are fresh lines of inquiry and a case worth pursuing, there is a young lady out there who deserves to be reunited with her parents - or a murder case that deserves to be pursued."