The groups - which recently released hit albums "Future Past" and "Music of the Spheres", respectively - will perform in front of a small audience of fans at BBC's Radio Theatre in Broadcasting House, London.
The shows will be broadcast live on BBC Radio 2, along with BBC Sounds and BBC iPlayer, on which they'll be available for 30 days after broadcast.
"We are so looking forward to playing for Radio 2 In Concert this December," said Duran Duran's Simon Le Bon. "The station has supported us and our music more than we could have hoped."
"So at last, we'll get to play songs from our new album, Future Past, along with Duran Duran classics at the wonderful BBC Radio Theatre, and add our name to the illustrious list of artists who've made it on to this legendary series."
Coldplay's Chris Martin added, "Playing live and finding connection with people is why we exist as a band so we're super excited to play Radio 2 In Concert."
"It's going to be a special night so please join us in person, on the radio or on BBC iPlayer."
Tickets for the shows, which take place on 2 (Duran Duran) and 7 (Coldplay) December, will be allocated via ballot, with audiences able to register to apply at www.bbc.co.uk/radio2inconcert. Applications close on 15 November.