The 15-year-old flew back to the UK more than a week after she left with her 30-year-old married maths teacher, Jeremy Forrest from Inverurie.
He has been arrested on suspicion of child abduction after the pair were found "strolling hand in hand" in the town of Bordeaux on Thursday.
In a statement, Forrest's solicitor Phil Smith said: "He has agreed to return to the UK as soon as possible without the need for protracted extradition proceedings."
Megan was seen boarding an EasyJet flight from Bordeaux to Gatwick airport yesterday afternoon, accompanied by a man and a woman.
It is understood she was reunited in private with her mother Danielle Wilson, who had earlier been seen leaving the family home in Eastbourne, East Sussex, by car.
A Sussex Police spokesman said officers intended to speak with Megan once she had met with her mother and stepfather Martin Stammers.
Yesterday, fresh reports emerged in the French media about the pair's trip. It was claimed Megan had used her 37-year-old mother's passport to flee the country with Forrest on a ferry from Dover to Calais, raising questions about border controls and security.
It was also reported that Forrest, who was born in Aberdeenshire, had told police the plan was to stay in France until Megan's 16th birthday, which is believed to be next June.
On his return he is likely to face questioning about his relationship with Megan, who at 15 is below the UK age of consent.
Forrest, who taught Megan at Bishop Bell Church of England School in Eastbourne, currently remains in police custody in France. It is understood it will be a number of days before he is returned to the UK and he will appear in court in France on Tuesday.
Megan's parents were in contact with their daughter by telephone after she was found but had remained in the UK while they awaited her return, a Sussex Police spokesman said.
An officer from Sussex Police's child protection team travelled to Bordeaux to meet Megan, while a detective inspector from the force was already in France as part of the ongoing search for the teenager.
The pair were spotted in Bordeaux by a member of the public who recognised Forrest from television coverage, said Chief Inspector Jason Tingley of Sussex Police.
It was the third potential sighting of the pair in the city, and they were tracked down shortly after midday on Friday.
Megan was reported missing when she failed to turn up for school last Friday, and it emerged she had travelled with Forrest to France the previous evening, sparking a well- publicised search.
On Friday the families of the pair expressed their relief that they had been found.
Speaking at a press conference, Megan's stepfather Martin Stammers said: "We just can't wait to be reunited with her. Our family are overjoyed at the outcome. As you can imagine it's been an absolute emotional rollercoaster."
He also requested that they be left alone in private to "bond as a family" after her disappearance.
Forrest's parents Jim and Julie Forrest, who had made a tearful public plea to the pair to get in touch, said in a statement: "We are pleased that Megan and Jeremy have been found safe and well. This has been an ordeal for all the families concerned.
"We would like to thank Sussex and the French police as well as the British media for their assistance.
"We are relieved that the search is finally over and everyone can now focus on a safe and secure return for them both."
Terry Boatwright, headteacher of Bishop Bell School, said everyone was delighted Megan had been found. He said: "Throughout the last week, finding Megan has been everyone's priority and a major focus of our thoughts and prayers in school.
"Clearly, much needs to be done now to support Megan and her family as they seek to return to some sort of normality and we will do all we can to play our part in that."
It was claimed concerns had been raised about the teenager's relationship with her teacher as early as February, when her friend told another teacher they had been seen holding hands.
East Sussex Council said it has launched an investigation.
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