The memorial, commissioned by her three sons Robert, Ben and Jack, is situated outside the original entrance to the world famous Cavern Club where the late singer and TV presenter had worked as a cloakroom girl.
The ceremony also marked the 60th birthday of the nightclub where The Beatles played in their early years.
Unveiling the statue, Robert Willis said his mother, who died aged 72, “never really appreciated getting old but now she will be forever young”.
He told onlookers: “We were overwhelmed by the incredible support after our mother died from the country but also, and especially, from the people of this great city.
“It was incredibly comforting and it moved us deeply and gave us hope at a time when we didn’t have much hope. It was something that none of us will ever forget.”
He said the sculpture, which was made locally, was not only a memorial to his mother but donating it to Liverpool was “a small gesture of gratitude and thanks to the people of this wonderful city”.
He continued: “What would our mother think of it? I think she would be incredibly proud. She would be flattered. She would have been incredibly honoured.”
He said: “It brings a smile because they have caught the joy. It’s based on a sixties design, the dress is chequered and it enabled us to put little stories like photos and lyrics hidden in there for people to check out.
“I’m just incredibly relieved that it turned out as well as it did. We are so happy with it, and I hope people enjoy it. And they did get the legs right, she had great legs. And also the nose – it’s the post-nose job nose which she would have insisted on.”
Andy Edwards, one of the sculptors, said “it’s the story of the birth of that period in Liverpool’s musical culture” and it was important the city remembered her.
The Cavern was demolished in 1973 to make way for a shopping centre but reopened ten years later on part of the same site using reclaimed bricks from the original building. The Beatles played hundreds of gigs there between 1961 and 1963. Cavern director John Keats said the club had remained relevant and people were “constantly surprised at who has played [here]”.
John Lennon’s half sister Julia Baird, said the role it played in musical history should not be underestimated and she thought Lennon “would have loved” to be part of the celebrations.
Thousands of well-wishers lined the streets of Liverpool for Black’s funeral after she died in August 2015.