Madeleine McCann disappeared from her parents' holiday apartment in the Portuguese resort of Praia da Luz in May 2007, shortly before her fourth birthday.
Since then her parents have campaigned tirelessly for the search to continue.
In a statement the couple said they understood and accepted the reason behind the decison to scale back the investigation at this stage.
They said: "We would like to thank all the staff from Operation Grange for the meticulous and painstaking work that they have carried out over the last four and a half years. The scale and difficulty of their task has never been in doubt.
"We are reassured that the investigation to find Madeleine has been significantly progressed and the MPS (Metropolitan Police Service) has a much clearer picture of the events in Praia da Luz leading up to Madeleine's abduction in 2007.
"Given that the review phase of the investigation is essentially completed, we fully understand the reasons why the team is being reduced.
"We would also like to thank the Home Office for continuing to support the investigation.
"Whilst we do not know what happened to Madeleine, we remain hopeful that she may still be found given the ongoing lines of enquiry."
Assistant Commissioner Mark Rowley said "every possible measure" was being taken to find out what happened to Madeleine, who would now be 12-years-old.
He said: "We still have very definite lines to pursue which is why we are keeping a dedicated team of officers working on the case. We have given this assurance to Madeleine's parents, Kate and Gerry McCann."
During Operation Grange detectives from the Met regularly travelled to the Algarve to liaise with their Portuguese counterparts and undertook a number of exploratory digs in the Praia da Luz area.
Police said they had also investigated more than 60 persons of interest.
A total of 650 sex offenders have also been considered as well as reports of 8685 potential sightings of Madeleine around the world.
In 2013 detectives working on Operation Grange announced they were looking into possible links between Madeleine's disappearance and bogus charity collectors who were knocking on doors in Praia da Luz at the time.
They issued a series of photo-fit images of suspects they said may have been hanging around the Algarve around the time Madeleine disappeared.