The 15-year-old from Eastbourne flew back to the UK on Saturday afternoon and was being reunited with her parents before talking to Sussex Police.
Teacher Jeremy Forrest, 30, has been arrested by French police on suspicion of child abduction.
The BBC's Andy Moore says a plane from Bordeaux has now landed in the UK
The pair were found in Bordeaux on Friday, after a sighting on Thursday.
'No protracted extradition'
Mr Forrest was arrested after the pair were traced.
Earlier, lawyers for the teacher said Mr Forrest would not fight extradition proceedings and had agreed to return to the UK as soon as possible.
Phil Smith, from Tuckers Solicitors, said in a statement: "He [Mr Forrest] has agreed to return to the UK as soon as possible without the need for protracted extradition proceedings."
The BBC's Luisa Baldini said Mr Forrest's cooperation with the authorities meant protracted extraditions could be avoided, but it would still be several days before he returned to the UK.
She said Mr Forrest was being held at a detention centre in Bordeaux and would appear before a local judge on Tuesday.
Mr Forrest's lawyers have said he is upset but is being treated well and with some sympathy.
Megan's parents have already been in contact with their daughter by telephone but remained in the UK to wait for their daughter's return, Sussex Police said.
'Emotional rollercoaster'
A police spokesman said police would talk to Megan after she had seen her mother Danielle Wilson and stepfather Martin Stammers.
Jeremy Forrest and Megan Stammers Jeremy Forrest and Megan Stammers were found in Bordeaux
Megan was reported missing by her family after she failed to turn up at Bishop Bell C of E School, in Eastbourne, on 21 September.
It later emerged she and Mr Forrest had caught a ferry from Dover to Calais the day before.
After they were found, Megan was taken into the care of British Consular staff and a Sussex Police child protection team officer who had joined her in France.
Her family said they were "overjoyed at the outcome".
Mr Stammers said: "As you can imagine it's been an absolute emotional rollercoaster."
He asked that they were left alone to "bond as a family" after Megan's disappearance.
BBC news