Promising "the hottest bands and artists in the world right now" the series is due to debut in the autumn.
It has yet to receive a title or a timeslot, but will be made by James Corden's company Fulwell 73, whose work includes the wildly-successful Carpool Karaoke series.
An initial run of six episodes has been commissioned.
Top of the Pops was also commissioned for half a dozen episodes in 1964 - but ended up running for 42 years, providing the BBC an unrivalled catalogue of performances by the likes of The Rolling Stones, Nirvana, Beyonce, David Bowie and Madonna.
It registered its highest audience in 1979, when more than 19 million people tuned in to see Dr Hook's When You're in Love with a Beautiful Woman topping the chart.
But by 2002, it had lost millions of viewers to 24-hour music channels like MTV. The show was eventually shunted to BBC Two before being cancelled.
Re-runs of old episodes continue to be screened on BBC Four, while the brand is resurrected for Christmas specials every year.
However, the new show is not envisaged as a successor to Top of the Pops and its top 40 format. Instead, it promises "live music performances, sketches and interviews".
BBC Music's Jan Younghusband suggested it would be a successor to one-off specials like Adele at the BBC and Michael Buble at the BBC.
Both shows included live performances and shareable moments, such as Adele auditioning to play her own lookalike.
Speaking to Music Week last year, Fulwell 73's Lou Pearlman described how the company would approach such a show.
"[If Top of the Pops was on now] it would have moments that would have ended up having 20 million views over the course of a few weeks," he said.
"Whether it's a live music show or not, whether it's performances or not, I just think there's something amazing to do in that space.
"There's nothing aimed at that weekend audience, nothing contemporary and relevant. There should be a show like that and we'd love to be the ones to make it."
The new BBC series will have Fulwell 73's Gabe Turner and former TFI Friday producer Suzi Aplin as executive producers, with more details to be announced in the summer.
"The BBC is the biggest music broadcaster in the UK and we are always looking for new ways to bring music to our audiences," said Bob Shennan, director of BBC Radio and Music.
"This series will be a fantastic opportunity to showcase the biggest and best UK and international bands and artists."
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Eleven years after the demise of Top of the Pops, a live, weekly music show is coming back to the BBC.