The 23-month-old boy, who suffered from a degenerative brain disease, died on April 28 at Alder Hey Childrens hospital, five days after doctors switched off his life support.
His case drew international attention following a long High Court legal battle after his parents Thomas and Kate Evans tried to take him to Italy for medical treatment.
Well-wishers lined up outside of Evertons Goodison Park ground in Walton Lane from the junction of Spellow Lane towards Queens Drive as the funeral procession passed around 11.30am this afternoon.
Supporters released balloons in his memory as they sang Youll Never Walk Alone.
Alfies father is a huge supporter of the Premier League club and had spoken of his hopes to take his son to watch the Blues in action.
Last week, Merseyside Police said they would send a small number of officers to the funeral to offer support for those attending but stressed it would not be open to the public or media.
In a post on the Alfies Army Facebook page, Alfies uncle Daniel Evans said: The funeral will be private due to familys wishes, we ask that no one turns up unless you have been personally invited by Thomas and Kate as theres a limited number of people who are allowed to attend, invitations are currently being sorted out for family and close friends.
He added: Thank you all for your support.
A vigil was held last Wednesday on what wouldve been the toddlers second birthday.
Doctors at Alder Hey stopped providing life-support treatment to Alfie last month after his parents lost two rounds of fights in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
During the protracted legal battle, Alder Hey Childrens 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.
Protesters attempted to storm the hospital on one occasion and blocked the road outside during demonstrations against the withdrawal of his life-support treatment.
Mourners finding every available space on Walton Lane, with some also gathered outside the Everton club shop. Alfies dad Tom said he had dreamed of one day being able to take his son to Goodison pic.twitter.com/kIUmPkRBwb
— Lorna Hughes (@lorna_hughes) May 14, 2018
Hundreds of people have lined the road outside Goodison Park to say goodbye to toddler Alfie Evans. This is where the public and press have been asked to gather as the funeral cortège passes. Its due here soon. pic.twitter.com/QLYIVKWH0w
— Rob Smith (@robsmithitv) May 14, 2018