"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."
Kyl served in the US Senate from 1995-2013 and decided not to run for re-election in 2012.
McCain died on August 25 after battling a rare form of brain cancer.
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