Andrew Bache, 51, from Portsmouth, was assaulted ahead of England's match against Russia in Marseille.
His family said: "He's progressing very slowly each day. He's been told he can come home."
Friends of Mr Bache, known as "Pepe", set up a web page in an effort to raise the Â£15,000 needed to fly him home.
Mr Bache suffered severe brain injuries and a cardiac arrest and had to be put in an induced coma before the game on Saturday 11 June.
The family said Mr Bache who was now "stable and breathing by himself", was expected to make the flight once his medical needs for the journey and in the UK were in place.
The family thanked all those who donated to the appeal which raised more than Â£27,000 for Mr Bache's ongoing medical treatment.
An England fan left seriously injured after being attacked by Russian supporters during Euro 2016 is well enough to fly home, his family says.