State Republican Party Chairman Tom Morrissey announced the selection of the venue on Tuesday.
The debate is being sponsored by the Arizona Republican Party and the Cable News Network. A date previously considered for the debate was Dec. 1.
The Republican National Committee authorized the debate during talks with Arizona Gov. Jan Brewer last summer.
Brewer said in a statement released by the state party that hosting the debate is a tremendous honor for Arizona that will allow its voters to get a close look at the candidates.