The corporation confirmed that the BBC London 94.9 presenter will take over the 5am to 6.30am slot from January 17 next year.
"I'm overjoyed to be joining the UK's most listened-to network as I'm a huge fan of Radio 2 - home of many of the country's most beloved presenters," Feltz commented.
"I'm utterly thrilled to be handing over to Chris Evans every morning - it's my idea of the perfect start to the day."
Bob Shennan, the controller of Radio 2 and 6 Music, added: "As well as being an accomplished and prize-winning radio presenter, Vanessa has a huge zest and passion for life in general, making her the perfect early morning show host. I'm convinced that she'll be the ideal companion to the millions of our earlybird listeners."
Feltz will also become the regular deputy presenter for Jeremy Vine's daily lunchtime show.
> Vanessa Feltz 'to return to TV on C5'