Sir Ian Botham, Dickie Bird and Micky Stewart joined family and friends for the service at St Chad's Church in Headingley, Leeds.
Close, who lived in Baildon, died aged 84 following a long battle with cancer.
Sir Ian described Close as "simply the best captain a young player could have ever wanted".
Close became the youngest player ever to represent England at 18 and went on to lead his country seven times in 22 Tests.
He leaves behind his wife Vivienne, a son and a daughter.
In a glowing tribute to Close, Sir Ian said: "He was the first man to congratulate you but he was also the first man to pull you down and take your legs away from you if you didn't get it right.
"But then in the evening he'd be the first guy to come up put his arm around you and say, 'Ian lad, come here, that's what I thought was wrong... but here's a drink, let's learn from that and move on'."
Speaking in an earlier interview, Mrs Close said she did not see her husband as a famous cricketer, he was "just Brian".
"I see him as my husband, the father of my children, someone who could be awkward, someone who I loved very much and who I know loved me."
She said one of his other talents was being a "wonderful dancer".
"He always maintained that cricketers should learn to ballroom dance because it keeps them on the toes.
"He was lovely but we argued because we both wanted to lead, which doesn't work in ballroom dancing; there's only one leader. He always won."
Colin Graves, the chairman of the England and Wales Cricket Board, former Yorkshire batsman Bryan Stott and former Yorkshire and England captain Ray Illingworth also attended the service.
Illingworth said: "We go back a long way. There won't be another like him. It's been shown by a wonderful turnout and the tributes. I think it's tremendous."
Bird said: "Brian was a tremendous captain and a wonderful man. I shall miss him and feel for his wife Viv and all her family.
"He was a hard man, believe me, but a good man."
A host of stars from the world of cricket have turned out for the funeral of former England, Yorkshire and Somerset captain Brian Close.