The news was relayed on the Radio 2 breakfast show by host Chris Evans.
Vine, whose brother is stand-up comic Tim Vine, told him: "How could I say no to the biggest show in TV? Yes, yes, yes and yes again to the sequins and the Samba!"
The 13th series of Strictly will start in September.
Vine, 50, hosts a daily news and music programme on Radio 2 and presents BBC One's Points Of View on Sundays, as well as Eggheads on BBC Two.
He told The Chris Evans Breakfast Show: "They asked me and I just thought I just turned 50 this year I've got to start dancing properly. I can't go into the dad dancing."
He added: "I just need to find some dancing shoes and identify my left foot. I am doing it for my two young daughters who jumped behind the sofa when I told them!
"It seems Dad on Strictly is more scary than Doctor Who!"
The other celebrities taking part will be announced over the course of the next few weeks.
The series will be presented by Claudia Winkleman and Tess Daly.
Last year's competition was won by new Xtra Factor presenter Caroline Flack, who beat celebrities including Saturdays singer Frankie Bridge and EastEnders actor Jake Wood to win the glitterball trophy.
BBC Radio 2 presenter and journalist Jeremy Vine is the first celebrity to be announced for the next series of Strictly Come Dancing.