Brown, 64, who lived in Bristol, made history in July 1978 when her daughter Louise was born at Oldham General Hospital.
Brown had been trying for a baby with her husband John for nine years before she became the first woman to give birth following in vitro fertilisation (IVF) treatment.
She died at the Bristol Royal Infirmary on June six with her family by her side, the BBC reported today.
A private funeral service was held in Bristol today.
She successfully conceived following pioneering treatment by Patrick Steptoe and Robert Edwards.
Louise Brown now has a son of her own. She leaves behind daughters Louise and Natalie, who were both born following IVF treatment, her stepdaughter Sharon and five grandchildren.
Her husband died five years ago.
Louise Brown said: "Mum was a very quiet and private person who ended up in the world spotlight because she wanted a family so much.
"We are all missing her terribly."
Dr Steptoe and Prof Edwards set up the Bourn Hall Clinic in Cambridge two years after Louise Brown's birth.
Speaking on behalf of Prof Edwards and the team at the clinic, chief executive Mike Macamee said: "Lesley was a devoted mum and grandmother and through her bravery and determination many millions of women have been given the chance to become mothers.
"She was a lovely, gentle lady and we will all remember her with deep affection."
