Crowds gathered on the streets of Liverpool to pay tribute to Alfie, with hundreds seen outside Everton's Goodison Park stadium while a procession passed by.
Evans was born on May 9, 2016, and was first taken to hospital in December of that year after suffering seizures.
Members of the public and "Alfie's Army" broke into applause as the funeral cortege passed the Goodison Park ground en route to a private burial in Liverpool.
Alfie Evans: Private funeral to be held
Doctors believed Alfie had a degenerative neurological condition, which has led to parallels being drawn with the case of Charlie Gard. His coffin was white with an Everton crest and toy soldiers on the side.
The 23-month-old, who suffered from a degenerative brain condition, died on April 28 five days after his life-support was turned off. Sleep well wee man.
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.
A private funeral for toddler Alfie Evans will be held later.
A key argument presented by Evans, 21, and James, 20, "was that they should decide what is best for their son", adds the broadcaster.
A vigil was held last Wednesday on what would have been the toddler's second birthday.
His parents, Thomas Evans and Kate James, wanted to take Alfie to a hospital in Rome, Italy, to continue his treatment in the hope he would recover. His parents had wanted to take him overseas to Italy for further treatment - but doctors said further treatment was futile and his life support was withdrawn last month.