Billy Monger, from Charlwood in Surrey, hit the back of a stationary car at Donington Park on 16 April.
The teen was trapped for 90 minutes, lost both of his lower legs and has spent nearly a month in hospital.
Monger, who turned 18 on Friday, said: "I'll be back racing as soon as I can."
He added: "All the support just makes me more determined."
His story has touched motor sport fans the world over who have raised in excess of £800,000 for his future.
The appeal exceeded its original £260,000 target after just six hours, raising £47,000 in one hour, Just Giving said.
Former Formula 1 world champions Lewis Hamilton and Jenson Button are among those who have given their backing.
Monger said he was "lost for words" by the worldwide appeal.
His father Rob said: "If he wants to get back in the car, that's fine by me. I'm not sure about his mum, but there we go."
His mother Amanda said the crash was "all your nightmares rolled into one" but the hospital staff had helped them through it.
Billy's sister Bonnie, 16, was among those at the scene of the accident and spoke to him to keep him calm while he was tended to by paramedics.
She said: "The first week was hard when he was in intensive care, but as soon as he woke up he was in such good spirits and that's lifted up everyone around him."
Kirsty Measures, a staff nurse who treated the young racer, said: "When Billy first came in he was quite unwell... he struggled to get to grips with what happened to him. But he has overcome it."
The family are due to return to their home in Charlwood on Saturday after Billy's discharge from hospital.
A teenage Formula 4 driver who had to have both legs amputated after a high speed crash has vowed to get back behind the wheel again.