Cindy McCain praised Kyl's selection, saying he was a friend of her family.
An ardent supporter of Kavanaugh, it comes as no surprise that Ducey tapped someone who will vote to confirm him to the Supreme Court.
Ducey said he hopes he will serve longer.
"Over the last few months, Sen". Jon Kyl is ready to cast a vote for Brett Kavanaugh to be nominated to the U.S. Supreme Court. She worked for Kyl as a national security adviser.
The appointment brings a more conservative bent to the Senate given Kyle's voting record and how it veers from that of McCain, a maverick who sometimes collaborated with Democrats on major legislation.
The Republican Kyl served previously as one of Arizona's two senators, alongside McCain.
Ducey said he received much advice about the appointment, "most of it unsolicited". But the best advice he received came from another governor, although he did not say whom. He said in a statement, "I've asked Sen". "I'm picking him because he's the best possible person".
Kyl, 76, the former Senate minority whip, served in the upper chamber from 1995 to 2013 and has been lobbying for a D.C. law firm since leaving Congress. He'll also have time to watch the Senate race to replace Jeff Flake - who won Kyl's old seat in 2012 - play out in November, with Republican Rep. Martha McSally facing Democratic Rep. Kyrsten Sinema.
Many names had emerged as possibilities to fill John MCCain's seat, including Cindy McCain, former Reps. They hold 51 seats with 47 Democrats and two independents who align with Democrats - unchanged from when McCain held the seat.
Kyl, 76, has committed to serve only until the end of the current congressional session on January 3.
The ex-senator said he was willing to serve through at least the end of the current Congress "to make sure that the business that is now ongoing is taken care of".
At a news conference where he was introduced as McCain's replacement, Kyl said he's only met Trump once, though he noted he is working for the White House by serving as Kavanaugh's so-called "sherpa".
What about re-election in 2020?
Kyl's appointment fulfills a couple of necessary criteria.
Arizona law requires the governor to appoint a member of the same political party to fill a seat opened by the departure of a senator. "There is much unfinished business, including confirmation of President Trump's nominees for judicial and executive branch positions, and I look forward to getting to work on behalf of my fellow Arizonans", said Senator Jon Kyl.
But Ducey's gubernatorial opponent, David Garcia, criticized the governor's pick.
Woods, who spoke during the memorial service for McCain in Phoenix last week, said his longtime friend's death led him to consider "whether I need to step up at this point in time".