Murphy, who penned The Worst Witch novels, died from cancer on August 18 with son Charlie and niece Isabelle at her side in a hospital in Cornwall, the statement said.
Charlie Murphy said: “I feel beyond lucky to have had a mum like mine and it’s impossible to summarise the ways her absence will be felt.
“She had a depth of character, a warmth and a life force like no other. I miss her so much already.”
As well as the Worst Witch novels, Murphy is known for the "Large Family" picture books.
Belinda Ioni Rasmussen, managing director of Macmillan Children's Books, said: "She had an unparalleled talent for storytelling through words and pictures.
"Without doubt, her picture books have become timeless children's classics.”
Jill Murphy was one of the UK’s most treasured author-illustrators.
From an early age she was drawing and writing stories, and by the age of eleven had made 90 books, which she kept and used to inspire children at events in later life.
She studied at Chelsea, Croydon and Camberwell Schools of Art, and wrote and illustrated her first published book, the bestselling The Worst Witch, while still only eighteen.
Murphy went on to create the award-winning Large family series in 1986, starting with Five Minutes Peace, and the series has to date sold over five million copies worldwide.
It was also successfully adapted for TV.