The Rising compete in the second tier United Soccer League (USL), but have applied for an expansion berth in MLS, who are planning to add four new teams over the next few years with two sides named later this year.
"After seeing first hand the potential for expansion of the sport in North America and getting to know the ownership group in Phoenix, I am convinced that I can help them develop their organisation on and off the pitch," Drogba said on the club website.
"I look forward to their continued success in the USL, and no city is better positioned than Phoenix for expansion into the MLS."
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Drogba, 39, played for Montreal Impact in MLS last season and the club and USL said they felt he would boost its exposure.
"We want our club and our city to be synonymous with international excellence, and Didier Drogba is a testament to Phoenix Rising FC's commitment to that mission," said Phoenix governor Berke Bakay.
USL president Jake Edwards was no less effusive.
"He will be a great ambassador for our sport, using his experience, talent and vision to benefit fans, as well as fellow players," Edwards said.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
