"I am deeply grateful to Senator Kyl for agreeing to succeed his friend and colleague of so many years," Ducey said in a Twitter message. "Every single day that Jon Kyl represents Arizona in the US Senate is a day our state is well-served."
In a press release, Ducey's office said Kyl will serve through at least the second session of the 115th Congress, which ends this year.
McCain's widow Cindy said in a statement it is "a great tribute to John that he [Kyl] is prepared to go back into public service to help the state of Arizona."
McCain died on August 25 after battling a rare form of brain cancer. He was known for his tough stance towards Russia and harsh criticism of Putin, supporting lethal arms supplies to Ukraine. McCain was also opposed to many of Trump's policies, even organizing resistance against his attempts to scrap Obamacare.