The pair - who are currently both in the West End company - will join the 9 to 5 The Musical tour in select cities from September.
Louise, who appeared on Strictly in 2016, will appear as Violet Newstead in Manchester, Milton Keynes, Liverpool, Glasgow, Edinburgh and Dublin.
She won't be the only Strictly star in the cast with 2017 contestant Brian Conley appearing as Franklin Hard in Milton Keynes.
Meanwhile, Love Island 2017 winner Amber Davies will play Judy Bernly in Birmingham, Manchester, Milton Keynes, Liverpool, Glasgow, Woking, Aberdeen, Cardiff, Sunderland, Edinburgh and Dublin.
Louise, Brian and Amber are all currently appearing in the musical in the West End.
Louise is scheduled to play her last performance in London on June 29 while Amber and Brian are set to continue performances until 31 August 2019.
With a score written by country music icon Dolly Parton, 9 To 5 The Musical is based on the 1980s comedy movie of the same name, which Dolly starred in.
The Oscar, Grammy and Tony award-nominated score features some of Parton's biggest hits, including the legendary '9 to 5', as well as original songs written for the show.