Police rushed to the scene of the incident, which happened in Wadworth, between junction two with the A1 and junction three of the M18 shortly after 5pm on Monday.
The driver, a man believed to be in his 60s, sadly died following the incident.
His family have been informed of the tragedy and are being supported by roads policing officers.
Enquiries into the circumstances surrounding the crash are still ongoing.
A National Highways spokesperson said: “Police investigations continued overnight and following vehicle recovery and debris clearance, National Highways is advising motorists to expect some delays during this morning’s peak.
“Emergency resurfacing work is taking place on the fire-damaged southbound carriageway and lane two northbound remains closed for ongoing barrier repairs.
“Lane one is now open northbound but drivers will experience some delays with a southbound diversion in place via the slip roads.”
National Highways tweeted: “The M18 remains closed in both directions within junction two near Doncaster.
“The road remains closed for specialist carriageway clean-up”.
Repair work on the roads isn’t expected to be complete until midday on Tuesday.
South Yorkshire Police said: “Drivers travelling southbound will leave the carriageway at Junction 2 and come back on to the M18 at the other side of the junction.
“All drivers are being informed so they can plan their journeys accordingly at this time.”
Traffic is being diverted through the exit and entry slip roads and there is still approximately two miles of congestion on approach in both directions.
On social media, people shared dramatic images and videos of smoke billowing from the large vehicle.
Some eyewitnesses reported hearing and seeing the lorry “blow up” and “explode”.