Janice St Fort, 58, died in hospital on Tuesday with her family at her bedside.
A statement issued by Rio, Anton and the family described Mrs St Fort as a “devoted mother” and “an inspiration”.
Rio Ferdinand lost his wife, Rebecca Ellison, to breast cancer in 2015. He filmed a documentary, Being Mum and Dad, earlier this year about how he and his three children have coped with grief.
“We are heartbroken to announce that our amazing mum Janice passed away today after an ongoing battle with cancer,” said the family statement.
“She was an inspiration to us all and was loved by everyone who knew her. She died at Guy’s Cancer Unit, London Bridge Hospital, with her loving husband Peter and us, her four children, at her bedside.
“She was a devoted mother to us all, and she was the most incredible grandmother to our children.
“The whole family are devastated. Our mum was the centre and the heart of our family and has supported us all through many difficult times, always with a smile on her face. Her strength and courage, as well as her great sense of humour and immense kindness, were never-ending.
“We would like to thank all the staff at Guy’s Cancer Unit for looking after our mum so well during her illness especially Marta and Joanna as well as everyone who has sent kind wishes to us all during this difficult time.”