Alfie's father Tom had spoken of his hopes to take his son to watch the Blues in action.
His coffin sported images of toy soldiers and the Everton club motif.
Flowers, pictures and messages left outside Everton's Goodison Park as the cortege of Alfie Evans goes past the ground in Liverpool, England.
The toddler lost his battle with a generative brain condition on April 28 after his case became the subject of a High Court battle over his life support.
Alfie's family requested that his funeral remained a private family affair.
His parents have thanked the community for their support but are asking for privacy during the funeral.
During the protracted legal battle, Alder Hey Children's Hospital said staff had experienced "unprecedented personal abuse" as it found itself at the centre of a "social media storm" as a result of the case.
The toddler, born on 9 May 2016, was admitted to Alder Hey Children's Hospital in Liverpool in December 2016 after suffering seizures.
Alfie died on April 28 at the age of 23 months.
A key argument presented by Evans, 21, and James, 20, "was that they should decide what is best for their son", adds the broadcaster.
His parents had fought a bitter battle with the hospital treating him, and the High Court, to allow them to take him overseas for further medical treatment.
Judges in the High Court, the Court of Appeal and the Supreme Court agreed with doctors and rejected a series of legal challenges by his parents to take him overseas.