Former tennis player Sue has been at the helm of the sports quiz series for 23 years, but will host her final episode with Matt and Phil as team captains next year.
Former England rugby player Matt, and former English international cricketer Phil have led their teams on the show for 16 and 12 years respectively.
A BBC spokesperson said: “We would like to thank Sue for her enormous contribution as the show’s longest reigning host over the last 23 years, and Matt and Phil for their excellent team captaincy over 16 and 12 years respectively.
“Together they have ensured A Question of Sport remains a firm favourite with the BBC One audience.
“Sue, Matt and Phil’s final series will be broadcast next year.”
The new presenter and team captains have not been announced.
Referred to by the BBC as “the world’s longest running TV sports quiz”, the first edition of A Question Of Sport aired in January 1970.
Sue took over as presenter from commentator David Coleman in 1997.