The six best-selling books - Zagazoo, Loveykins, Jack And Nancy, Snuff, Angel Pavement and Mrs Armitage On Wheels - will form animated series Quentin Blake's Box of Treasures, set to air on CBBC in December 2023.
Mission: Impossible and Shaun of the Dead star Pegg, and Gavin & Stacey's Steadman will be joined in an all-star voice cast by Adrian Lester (Hustle, Trigger Point) and Nina Sosanya (Teachers, W1A).
Lester will narrate the series, Steadman plays Mrs Armitage, Sosanya is Angela Bowling in Loveykins, and Pegg will voice lead roles in Zagazoo, Snuff and Angel Pavement.
Patricia Hidalgo, director of BBC children’s and education, said: "When it comes to storytelling for children, the UK has a rich heritage and history of creativity and Quentin Blake is known around the world for his unique talent.
"His imagination has brought magic to the lives of so many people, both young and old and it is an absolute privilege to be involved in this project.
"We’re delighted to be working with such a phenomenal, diverse cast of actors that will bring these beautiful characters to life for family audiences to enjoy on the BBC."
Sir Quentin, 89, has been writing and illustrating books for seven decades, working on more than 500 titles.
He is well known for his collaborations with the late children's author Roald Dahl.
Although viewers will have a while to wait to see the Box Of Treasures series in December 2023, there is a new Julia Donaldson animation to look forward to on BBC One this Christmas.
The children's author is continuing her BBC festive collaboration with another adaptation of one of her stories, this time The Smeds and The Smoos featuring the voices of Bill Bailey, Adjoa Andoh, Rob Brydon, Sally Hawkins and Meera Syal.
It is expected to air on BBC One on Christmas Day.