George McGowan, 19, was taken to hospital after the crash with the silver Volkswagen EOS on June 12 at 8.23pm in Leominster Road, Paulsgrove.
The Paulsgrove-based teenager was treated in Southampton General Hospital but died on June 22, police said today.
His family said: ‘George was a loving son, brother, grandson, and a friend to many.
‘George was a character who will be truly missed by his family and friends.’
Hampshire police said enquiries are continuing but no arrests have been made.
‘We would ask the public to not speculate on the circumstances while our investigation continues,’ a spokesman said.
Anyone with information should call 101 quoting 44210230490.
The e-scooter involved is not part of the trials run by Voi and Portsmouth City Council.
Councillor Lynne Stagg, transport boss at the council, told the BBC: ‘I am deeply saddened to hear of the tragic death of a private e-scooter rider and want to extend my sincere condolences to their friends and family.’
A message from the Editor, Mark Waldron