The couple, named locally as Jack Nunn and Hannah Elsworth, were reportedly travelling along Huddersfield Road towards Barnsley town centre at around 1.30am when the car struck the kerb and collided with a tree.
Both were pronounced dead at the scene after the car, a white Audi, burst into flames.
Residents reportedly rushed from their homes to douse the flames with buckets of water.
Floral tributes were later laid at the scene, as the road was closed until Sunday afternoon.
Family members have since set up a Just Giving page aiming to raise £2,000 for the NHS in memory of the couple.
People were also asked to light candles on Sunday night and a balloon release is planned to take place at Locke Park at 5pm next Friday.
In dozens of posts by friends and family, Jack and Hannah were described as a ‘beautiful’ couple.
Jack, 24, was a tyre fitter and co-owner of JJ’s Tyres on Wombwell Lane, Stairfoot - which announced it would be closed until further notice.
“My heartfelt condolences go to both families,” said his business partner on the firm’s Facebook page.
“We are all in complete shock and absolutely devastated.”
Hannah, 22, was a nurse at Barnsley Hospital, where tributes were also paid with the hospital chapel open for people to light candles on Wednesday.
“Barnsley Hospital is deeply saddened by the loss of our much-loved colleague and her partner,” said a spokesperson.
“Our thoughts and heartfelt condolences are very much with their family, friends and colleagues at this difficult time.”
Dean Brissett, Hannah’s former form teacher at Holgate school, said: “I also knew Jack from the Holgate days but I never taught him.
“The pair looked like they were going places and had a bright future. But unfortunately, it is not to be.
“Two young people taken well before their prime.”
South Yorkshire Police officers are appealing for witnesses or those with dash-cam footage that may establish the circumstances of the incident.
Anyone with information or footage is asked to call 101 quoting incident number 95 of June 21.
Enquiries are ongoing.
Visit www.justgiving.com/crowdfunding/amy-swift to donate.