Soap star Kelvin Fletcher and TV favourite Dermot Murnaghan will also take part in the Chris Tarrant quiz. All three celebrities will be joined by their siblings or children and will be aiming to raise money for their respective charities.
Redgrave and his 14-year-old son Zac are competing for the Sparks charity, while Fletcher and his 15-year-old brother Brayden are helping The Cardiomyopathy Association.
Murnaghan is competing with his 15-year-old daughter for Operation Florian.
"I am thrilled to be taking part in the show with my son Zak. I am sure it will be a challenge but I think we will be a strong team and we are looking forward to it. It will be great to help raise money for my chosen charity Sparks," said Redgrave.
Celebrity Who Wants to Be a Millionaire? School's Out will be broadcast on ITV1 on Sunday, August 26.