The presenter announced the news on his show this morning, stunning his colleagues.
He told them: "I've deceived you all for a long time because I've been sworn to secrecy."
He joins other names including Bafta-winning naturalist Steve Backshall and EastEnders bad boy Jake Wood in the new series of the BBC ballroom show.
Also in the running for the glitterball trophy are Mark Wright, who shot to fame on reality show The Only Way Is Essex, singers Simon Webbe and Frankie Bridge, former rugby player Thom Evans, presenter Alison Hammond, tennis matriarch Judy Murray and actress Sunetra Sarker.
The new series will be the first one without veteran host Sir Bruce Forsyth, with Tess Daly and Claudia Winkleman sharing the presenting job.
Mills, who has been with the station for more than 15 years, said: "My listeners are so used to me playing pranks that they're probably going to think this is just another one. It's not, I really am doing this!
"I'm honoured be part of the biggest show on television and hoping this could be the start of a brand new skill for me.
"When I was younger, my Nan danced the foxtrot and waltz and it would be great for me to learn those dances, but I will be out of my comfort zone.
"Whatever happens, I'm really looking forward to the weekly fake tans!"