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.

James Botham - the son of former Cardiff rugby player Liam - is in the Wales Under-18 team to play Scotland in Swansea on Friday.
Sir Ian, 60, does not find it strange that his grandson will be wearing red.
"He was born in Cardiff. He always wanted to play for Wales for as long as I can recall," said the ex-all-rounder.
"I'm really looking forward to it. I think it will be wonderful, a great occasion for James and one that I think he's very excited about, as are the family. I've got a red shirt with me."
Botham, who took 383 wickets and scored 5,200 runs in Tests for England, will watch James make his debut on at St Helen's - where he played county cricket against Glamorgan for Somerset.
James Botham is one of four players making their debuts for Wales, along with Harri Dobbs, Ben Thomas and Dane Blacker.
The match is part of a series which culminates in a game against England Under-18s on 6 April.
Sir Ian said he had not been tempted to persuade James to switch allegiance.
"Never, it's nothing to do with me," he added.
"I'm grandad, and grandad is going to come down and watch him and support him every game. Whether he's playing or on the bench it doesn't matter - all the family that can get down here will be here.
"And when Wales play England my allegiances would be with my grandson."

Having resumed on 55-1, the hosts lost Gary Ballance (45) and Andrew Lyth (39) early on, before Andrew Gale (67) and Jonny Bairstow steadied the innings.
Bairstow was trapped lbw by Chris Jordan after the break, while Chris Liddle removed Jack Leaning cheaply.
But Gale and Bresnan (50 not out) helped their side reach 298-9 at stumps, a lead of 301.
Sussex would need at least a draw to secure their Division One status for next season if rivals Hampshire can complete victory at Nottinghamshire on Friday.
The visitors started the third day strongly with the ball as Ballance and Lyth both played onto their stumps in the morning session.
Gale's patient innings put Yorkshire back on the front foot, and also saw the 31-year-old surpass 1,000 runs in the County Championship this season.
However the captain's 131-ball knock was finally ended when he was caught by Jordan off the bowling of Liddle, but Bresnan's half-century left Sussex in danger of playing Division Two cricket for the first time since 2010 next season.
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.
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England cricket legend Sir Ian Botham is looking forward to supporting his grandson James when he makes his rugby debut for Wales.
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Andrew Gale and Tim Bresnan hit half-centuries for Yorkshire at Headingley to deepen Sussex's relegation fears.