The team of detectives is said to have had no involvement in that investigation which ended in 2008 and was heavily criticised in the British media.
The new inquiry - which will run separately, but alongside the probe by British police - follows an internal review of the case since March 2011.
Portugal's public prosecutors approved the move after a request from officers in Porto who have identified new lines of inquiry, witnesses who were never questioned during the original probe and several issues they want to clarify.
A spokesman for the Attorney General's office said: "The Public Ministry has determined the reopening of the inquiry relating to the disappearance of Madeleine McCann following a request from the Policia Judiciaria."
Madeleine's parents Kate and Gerry said they were "very pleased" at the decision by Portuguese authorities and hoped that it would uncover "the answers we so desperately need".
"We hope that this will finally lead to her being found and to the discovery of whoever is responsible for this crime," the couple said.
"We once again urge any member of the public who may have information relating to Madeleine's abduction to contact the police in Portugal or the UK.
"Please be patient and respect the work of the police as they endeavour to find the answers we so desperately need."
The lawyer for the McCann's in Portugal, Rogerio Alves, said: "While it is not known what happened to Madeleine, the matter is not closed.
The reopening of the case is excellent news, it creates a new perspective on the case and gives hope to the parents. The result is that we all hope Madeleine is found."
Detective Chief Inspector Andy Redwood, who is leading the Scotland Yard team, Assistant Commissioner Mark Rowley and Mr and Mrs McCann met officers in Lisbon last week to be briefed on the Portuguese case.
Sky's Martin Brunt said the development would "boost the manpower" now applied to the case.
"This of course is what Madeleine McCann's parents have always wanted," he said.
"They were very disappointed when it was shelved after 15 months - after their daughter disappeared - the investigation having got nowhere.
"They were distraught at that, have argued ever since that it should be reopened and now they have got that wish."
He added: "There is an awful lot of work still to be done, there are lots of people to be tracked down and interviewed, and at least now the Portuguese detectives who will be re-engaged on this can join Scotland Yard in doing that."
Carrie-Marie Bratley, who works for the Portugal News in Lagoa, in the Algarve, told Sky News the Portuguese detectives "were chosen for their emotional and physical distance from this case in the hope that maybe they could go over it with a fine-tooth comb and come up with something, which it seems they may have done."
The team is separate to the group of six Portuguese officers based in Faro who have been assisting the Metropolitan Police.
The move to re-examine the case in the country where Madeleine went missing comes after a fresh appeal for information was aired in the UK, Holland and Germany.
Scotland Yard received more than 2,400 phone calls from across Europe following the broadcast of a reconstruction of events leading up to the three-year-old's disappearance in 2007.
They have released two e-fit images of a man they want to speak to in connection with the case based on the accounts of two witnesses.
Both described seeing him in Praia da Luz at around 10pm on May 3, as Madeleine's parents dined at a nearby tapas restaurant with friends.
Four other e-fits based on witness accounts of men seen in the area, some of whom may have been working as "charity collectors" who may or may not be genuine, were also released.
An appeal is also due to air on Irish television later this month.
Home Secretary Theresa May said the collaboration between British and Portuguese police officers was "starting to bear fruit" and hoped it would lead to a "resolution".
