Hundreds of people poured into two churches to pay their respects to the lay preacher and retired social worker, who was murdered on his way to a Christmas Eve service.
VIDEO: Press the play button to watch our video report.
The funeral service took place at St Saviour’s Church in High Green, Sheffield - a few hundreds metres from where the 68-year-old was attacked.
The service was also shown via video link in the packed St Mary’s Roman Catholic Church, just down the road.
Widow Maureen told the congregation of her love for her husband - ‘a truly beautiful man’.
She described how they told each other of their love the morning before he was attacked.
Mrs Greaves said: “Alan bought me my last bunch of flowers on Christmas Eve morning. When I went to thank Alan and give him a kiss, he said, ‘I love you so much Maureen, so much, and I’m so glad that I married you’.
“I answered with the same.”
The funeral cortege had arrived outside St Saviour’s, where Maureen was joined by family members to watch the wicker coffin carried into church.
There were no flowers in the black hearse, although the lead mourner carried four red roses ahead of the pallbearers.
Members of the public who could not get into church gathered in freezing temperatures outside to listen on speakers.
Mr Greaves suffered head injuries on Greengate Lane, close to his home at around 11.10pm on December 24.
He died in hospital three days later.
Speaking ahead of the funeral Maureen, to whom he was married for 40 years, said they had a ‘truly wonderful marriage’.
She said: “His death was a very great shock and I wasn’t prepared for it. I wasn’t expecting him to die.
“The fact that the community have responded so well has been a comfort.
“He truly was a gentleman and he was someone whose love and compassion came over very clearly to people.”
Mr Greaves was attacked on Christmas Eve as he made the short walk from his home in High Green, to St Saviours where he played the organ.
Just weeks before his death, Mr Greaves had helped establish a new food bank project for those in need in South Yorkshire.
The couple both worked for Church Army and gave up huge amounts of time helping and supporting others.
They got married in Sheffield in 1972 and had four children together.
Mrs Greaves said: “Obviously the house is full of memories. One of the saddest memories is that the piano has fallen silent.
“It is not something I’m going to get rid of, I will keep it and Alan’s two daughters can play the piano and one day one of them might inherit it.”
She added: “I can look back on 40 years that have been really truly wonderful, even with all its disappointments and things that happen in any marriage.
“It wasn’t a perfect marriage, but it was a marriage that was perfect in the fact that we stayed in love with each other.”
Since his death, Mrs Greaves said the family had been touched by the support from people affected by her husband’s death.
Mrs Greaves said: “It has been very overwhelming and humbling.
“Whenever I have walked on the streets people have come to me to give me a hug to say how sorry they are and especially to ask if they can do anything for me.
“Some people that have done that I know well - others have been complete strangers.”
She has written the eulogy to her husband and will read it later on today.
Two men have been charged with Mr Greaves’ murder.
Jonathon Bowling, 22, and 21-year-old Ashley Foster have both been remanded in custody.