The pair will reprise their roles as Violet Newstead and Franklin Hart Jnr respectively ahead of the show ending its West End run on May 23.
Redknapp will return from Monday, February 10 through to May 23, excluding performances between March 12 and 28. She replaces Caroline Sheen who will play her final performance on Saturday, February 8.
Conley will reprise his role from Monday, March 2. He replaces David Hasselhoff who will play his final performance on Saturday, February 8. Sean Needham will play the role between Monday, February 10 and Saturday, February 29.
Louise and Brian will join Chelsea Halfpenny as Judy Bernly, Natalie McQueen as Doralee Rhodes and Bonnie Langford as Roz Keith.
Completing the cast are Victoria Anderson, Alexander Bartles, Stephanie Chandos, Conor Crown, Alexander Day, Rhiane Drummond, Demmileigh Foster, Ross Lee Fowkes, Molly-May Gardiner, Llandyll Gove, Ben Irish, Jenny Legg, Sean Needham, Jon Reynolds, Ricardo Spriggs, Antoine Thomas-Sturge, Sasha Wareham and Emily Woodford.
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.
It tells the story of workmates Doralee, Violet and Judy who push back against sexist supervisor Franklin Hart. 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.
As well as the West End production, 9 to 5 The Musical is set for a second UK tour in 2020.