McSally will take the seat next month after the departure of Sen. John Kyl, who has filled in since McCain's death in August.
The decision revives McSally's political career after she lost a close race for the state's other Senate seat to Democrat Krysten Sinema last month.
McSally was criticized for not mentioning McCain's name during Trump's signing of the John S. McCain National Defense Authorization Act. McSally has since apologized. Cindy McCain later tweeted she hoped McSally would continue her husband's example of 'selfless leadership.'
"My husband's greatest legacy was placing service to AZ & USA ahead of his own self-interest," she wrote. "Arizonans will be pulling for her, hoping that she will follow his example of selfless leadership."
Ducey said he expects Sinema and McSally to work together in the upper chamber. His announcement also means Arizona, which prior to Sinema's election never sent a female senator to Washington, now has two women in the chamber.
McSally is also the 25th woman who will be in the Senate at the start of the next Congress, a new record.
"All her life, Martha has put service first -- leading in the toughest of fights and at the toughest of times," he said. "With her experience and long record of service, Martha is uniquely qualified to step up and fight for Arizona's interests in the U.S. Senate."
McSally said she's "humbled and grateful" by the "opportunity to serve." She will stay in the seat until 2020 when Arizona will hold a special election for the vacancy. McCain was re-elected in 2016 for a term set to last until 2022.