The three-year-old died after being hit by a car in the capital’s Morningside suburb.
Hundreds of locals showered his funeral cortege with flowers close to the spot where he was struck in emotional scenes.
Tributes included 400 red roses placed on his hearse as it made its way along Morningside Road.
In a statement previously released by the family, they said: “Xander was a very happy, bubbly, intelligent little boy who was very dearly loved by his parents Victoria and Paul.
“Xander was a real chatterbox who just loved books, playing with all sorts of vehicles and his Lego.
“He really enjoyed life and he enriched the lives of everyone he met.
“Victoria and Paul are devastated and feel as if their hearts have been ripped out.
“Xander will be so very sorely missed by them both and all his family and friends in Scotland and Northern Ireland.
“What will we do without you, Xander?”
The sombre procession was led by a funeral director dressed in a top hat, as well as a police car and a fire engine.
A floral wreath reading ‘Xander’ could be seen in the back of the hearse.
Local florist Quate & Co handed out 400 roses to those who had gathered so they could be placed on the hearse as it passed.
A fundraiser was launched to help the family, and more than £25,000 had been donated by Thursday.
Xander had been out for a walk with his mum Victoria, 37, when they were both hit by a car last week.
They were raced to hospital but tiny Xander died a short time later.
His devastated mum was treated for her injuries but has since been released.
The 91-year-old female driver of the car was uninjured and a police probe into the horror incident remains ongoing.
A Red Kia mounted the pavement on Morningside Road and crashed into the mother and child on June 29.
Inspector Roger Park of Edinburgh City Road Policing Unit added: “Our thoughts remain with the family of Xander at this incredibly difficult time.
“Enquiries into the crash are ongoing, a full forensic collision investigation was carried out at the time and officers continue to look at CCTV and dash-cam footage as well as tracing and speaking to witnesses who have come forward.
“I wish to express my sincere thanks to the members of the public who intervened and assisted in the immediate aftermath of this tragic incident and to the police and other Emergency Services who were on the scene.”
The GoFundMe page was launched by heartbroken community members after little Xander Irvine died on Tuesday afternoon.
To donate to Xander’s family fundraiser, please click here.