Officers searching for Emma Sillett, 41, and five-year-old Jenson Spellman recovered two bodies from a reservoir on Thursday (22 Nov).
The pair were reported missing shortly before midday on Tuesday (20 Nov) after they left a McDonald’s restaurant near their home in the village of Dinting, near Glossop.
They were last seen travelling along the A560 Stockport Road in Greater Manchester in Ms Sillett’s Peugeot 308.
Staff at Simmondley Primary School, where Jenson was a pupil, had not seen him since Monday.
The discovery of two bodies came hours after officers found Ms Sillett's black Peugeot 308 hatchback close to the reservoir, near Tintwhistle, Derbyshire.
The man-made lake is less than three miles from her home in the village of Dinting, near Glossop.
Post-mortem examinations are now due to take place and the force said it was not looking for anyone else in connection with their deaths.
Assistant Chief Constable Kem Mehmet yesterday (thurs) said: “At 11.35pm on Tuesday, November 20, we received a call to report Emma Sillett and Jenson Spellman as missing.
"Since then extensive enquiries have been carried out by police and external agencies to locate 41-year-old Emma and five-year-old Jenson safe and well.
"After a detailed search by specialist officers, it is with great sadness, that the bodies of what are believed to be Emma and Jenson were located at Valehouse Reservoir earlier today."
Mr Mehmet said there is no indication anyone else was involved in their deaths.
"At this time our enquiries are ongoing and officers will be in the area for some time to come," he added.
"Whilst in the investigation is in its early stages we have no indication that any other person is involved in their deaths.
"Further enquires are ongoing to establish the full facts of the case.
"I would like to take this opportunity to pass on my own condolences, as well as those of every officer in Derbyshire, to the family and friends of Emma and Jenson."