Jones will takeover Katharine McPhee in the lead role as Jenna while Roberts will replace Laura Baldwin in the role of Dawn.
They will make their official debuts in the role on June 17, although Jones has already gone on for McPhee this week.
Jones rose to fame on The X Factor in 2009 and represented the UK at Eurovision in 2017. Her stage credits include Rent, Legally Blonde and A Christmas Carol.
She said on her social media pages: "I will never stop crying 😭 From June 17th I will be playing the role of Jenna in @waitresslondon 🥧 This show is absolutely stunning and I cannot believe my luck... I get to tell Jenna’s story every day and sing the gorgeous @sarabareilles tunes nightly. Genuinely, my dreams are coming true"
Roberts is best known as a member of former pop group The Pussycat Dolls and last year made the final of Strictly Come Dancing.
She shared with her fans: "Got some sweet news! I'm going to be playing Dawn in @WaitressLondon from 17th June. Yasss to some comedy singing and dancing fun!! Can’t wait! Hope to see you there"
Producers previously announced that American singer McPhee will play her final performance on 15 June.
Baldwin will return to the cast at the end of the summer, with Waitress currently booking until October 2019 at the Adelphi Theatre.
With a score by Sara Bareilles, a book by Jessie Nelson and direction by Paulus, Waitress features a ground-breaking, all-female lead creative team.
It tells the story of Jenna a waitress and expert pie-maker who dreams of a way out of her small town and rocky marriage.
Other cast include Marisha Wallace as Becky with Peter Hannah as Earl, David Hunter as Dr. Pomatter and Shaun Prendergast as diner owner Old Joe.
Completing the current cast are Kelly Agbowu, Piers Bate, Nicole Raquel Dennis, Michael Hamway, Peter Hannah, Stephen Leask, Chris McGuigan, Olivia Moore, Nathaniel Morrison, Sarah O’Connor, Leanne Pinder and Charlotte Riby.