Madeleine McCann, from Leicestershire, was 3-year-old when she disappeared from Praia da Luz in the Algarve, Portugal, in May 2007.
Portugal’s attorney-general said “new elements of evidence” justified the “continuation of the investigation”, which was shelved by police in 2008.
Madeleine McCann’s parents said they hoped for “the answers we so desperately need”.
Scotland Yard began a review of the case in May 2011 – codenamed Operation Grange – and opened a formal investigation in July 2013.
They said the Portuguese decision followed the “discovery of new lines of inquiry as a result of an internal review of the original investigation by the Portuguese Policia Judiciaria”.
It comes after Scotland Yard said at a briefing earlier this year that the Portuguese inquiry would not be re-opened until judges there were convinced there were solid grounds to do so.
Assistant Commissioner Mark Rowley and Detective Chief Inspector Andy Redwood met senior Portuguese police last Thursday in Lisbon for a briefing on the new lines of enquiry which they said were “separate” to those being followed by the Metropolitan Police (Met).
Madeleine’s parents, Kate and Gerry McCann, were also briefed on the plans to apply to reopen the investigation.
They said they were “very pleased” the Portuguese inquiry, which will run in parallel with the Met operation, was being reopened.
“We hope that this will finally lead to her being found and to the discovery of whoever is responsible for this crime,” they 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.”
Mark Rowley, assistant commissioner for specialist crime and operations, said the meeting was “very positive” and both forces had a “shared determination” to solve the case.
“I believe that we have the best opportunity yet to finally understand what happened to Madeleine,” he said.
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