The show, which opens on 12 November 2014 (previews from 8 November) for an eight-week season, will be the first to play the Dominion, where We Will Rock You closes this weekend, following its refurbishment.
Adapted from the much-loved film, White Christmas tells the story of two ex-army pals as they team up with a pair of sisters to put on a show to save their former General's remote Vermont ski lodge that's fallen on hard times.
The score includes "Blue Skies", "The Best Things Happen When You're Dancing", "Count Your Blessings" and the iconic title song.
Aled Jones, who rose to fame as a choirboy with his rendition of "Walking in the Air", said: "I am absolutely delighted to be making my West End musical theatre debut in such a well-loved musical... And I'm looking forward to sharing Strictly Come Dancing stories with Tom - I taught him everything he knows."
Chambers, who returns to the West End for the first time since Top Hat, added: "I'm a huge fan of Irving Berlin's music and it'll be a great pleasure to be back in my tap shoes again."
White Christmas will be presented at the Dominion Theatre by Michael Rose and U-Live for White Christmas Onstage Limited, in association with Paramount Pictures.