Len Goodman will also continue as a judge on the tour despite announcing the current TV series will be his last.
Rani replaces Mel Giedroyc, who has already signed up to co-present a new BBC One talent show in 2017.
Giedroyc and Graham Norton will front Let It Shine - a nationwide search for singers and actors to play Take That in a new musical.
Gary Barlow, Dannii Minogue, Martin Kemp and Glee's Amber Riley will be judges on the show.
Giedroyc announced last week that she and Sue Perkins will leave The Great British Bake Off when the programme moves to Channel 4 after the current series.
Rani, who has also previously co-presented Watchdog and Four Rooms, competed on Strictly Come Dancing last year, finishing in fifth place.
Also appearing on the Strictly Come Dancing tour alongside Goodman will be Craig Revel Horwood and guest judge Karen Hardy.
The tour will also feature many celebrity contestants from the show, but it has not yet been confirmed which.
The live shows, which Revel Horwood will direct for the seventh year, will see the judges score the contestants' dances and arena audiences able to vote for their favourites.
Goodman said: "The live tour always has such a great atmosphere and the tenth anniversary tour will definitely be one to remember, especially as this will come as I complete my final year on the TV series as head judge."
The 30-show tour will open in Birmingham on 20 January.
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Countryfile presenter Anita Rani will host the next Strictly Come Dancing tour, which begins in January.