Liam Fuller, from Coventry, West Midlands, heard the van's jingle as he played with a football in a relative's front garden on Thursday, opened the gate and ran into the road.
He was taken to Coventry and Warwickshire Hospital but died of head injuries shortly after admission.
Liam's mother Michaela Fuller, 27, yesterday described the moment she heard he had been involved in an accident.
"Someone told me he was in hospital and I just burst into tears," she said. "He is my only son.
"I got together his little pyjamas and took them to the emergency ward but it was all too late.
"He was a cheeky little chap but so beautiful. My world has fallen apart."
Michaela's partner Jason King, 24, said: "We will miss him so much."
Liam's aunt, Miss Sheila King, said Liam was playing football in another aunt's front garden in the Wood End area of Coventry when he heard the ice cream van.
"He kicked the football away, unlatched the gate and went to greet the van.
"His aunt only let him out of her sight for a minute but when she looked out she saw him lying under the van.
"She blames herself. This is an absolute tragedy."
Linda Taylor, 34, who was near the scene of the accident, said a crowd of children had run towards the van as it approached, and they had all wanted to be at the head of the queue.
"The first thing I heard was someone shouting and I thought they were shouting at the children to calm down.
"I came out of the house and I saw little Liam lying there.
"I turned him on his side and felt his pulse and then put a towel over him to keep him warm."
Ms Taylor said Liam had been staying with his aunt, Kerry Fuller, and added: "Kerry was kneeling. She was hysterical, just in floods of tears. She was desperate for Liam to survive."
Mary King, 51, the boy's grandmother, said Liam was a mischievous but lovely little boy who loved the Teletubbies.
"He had Teletubbies bedsheets, Teletubbies curtains and Teletubbies clothes. I can't believe he's been taken away from us."
Miss King said the child had been warned about running into the road when he heard ice cream vans coming.
"He just loved lollipops and ice creams so much and would jump for joy when he heard the ice cream jingle," she said.
"We had told him before never to run into the road but this time he couldn't help himself."
West Midlands police are investigating the incident and are appealing for witnesses.
The driver of the ice cream van has not been named.