Pitch Battle - a working title - will feature all musical styles, including rock, folk, gospel and a cappella.
The show will feature "riff-offs" between singing groups - an idea made famous by the popular Pitch Perfect films.
The series will consist of six hour-long episodes, the BBC said.
Pitch Battle will feature an a capella round as well as a soloists challenge across its five heats, before a winner is crowned in the live final.
Kate Phillips, the BBC's controller of entertainment commissioning, said the new show would have "shed loads of sass and spirit".
"There are millions of people in the UK of all ages and backgrounds who sing simply for the love of it, for the joy and sense of community it creates," she added.
The show was commissioned by Phillips and Charlotte Moore, director of BBC content.
It is the second music-based Saturday night series to be commissioned by BBC One in recent months.
From January the channel will also air Let It Shine, a talent contest searching for actors and singers to play Take That in a musical about the band.
The announcement of the two new series follow the confirmation that The Voice will move to ITV in the new year.
A cappella singing has become increasingly popular since 2012, when the first Pitch Perfect film, starring Anna Kendrick and Rebel Wilson, became a surprise hit.
The success of the movie led to a sequel, which topped the box office both in the US and the UK.
The new-found popularity of a cappella has also led to the success of Pentatonix, a vocal harmony group from Texas.
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A new Saturday night entertainment show searching for the UK's best singing group will launch in 2017, BBC One has announced.