Alex Firth, who was in his 30s, was killed in the collision on Sunday April 2, while his wife and 10-year-old son were seriously injured.
The crash involved a HGV and four cars and happened on the A637 Claycliffe Road in Barugh Green at 1.30pm.
Alex worked at the Seacroft Delivery Office and a colleague said he was a "highly valued and well-liked member of the team".
They added: "Not only was he a great postie but a fantastic lad who had a lot of time for everyone.
"We are all deeply saddened by this tragic incident, and our thoughts and prayers go out to Alex’s family and friends.”
South Yorkshire Police are appealing for anyone who witnessed the crash to come forward.
In a statement, a police spokesperson said: "The driver of a Vauxhall Astra involved in the collision, a man in his 30s, suffered serious injuries and was sadly pronounced dead at the scene.
"His family are being supported by specially trained officers.
"The front passenger in the Vauxhall Astra, a woman in her 30s, was conveyed to hospital via ambulance with serious injuries and remains in a critical condition.
"The rear seat passenger, a 10-year-old boy, was also conveyed to hospital with serious injuries, and is now in a stable condition.
"It is believed that a red Mini, a white Mercedes and a black Kia were also involved in the collision, alongside the HGV. None of the occupants of these vehicles received serious injuries during the collision.
"Officers are keen to hear from anyone who witnessed the collision, or who may have dash cam footage of the collision or cars prior, to call 101 quoting incident number 407 of 3 April 2022. Any footage can be emailed to [email protected] with the incident number in the subject line."