If he wins the Democratic nomination, Kelly would take on Republican Martha McSally in what is expected to be one of the most closely contested Senate races of the 2020 election.
Kelly described himself as an independent-minded centrist who will take a scientist's data-driven approach to solving problems such as climate change, wage stagnation and health care affordability.
"You see a lot of partisanship in Washington and a lot of polarization, and to some extent we've created that," Kelly told The Associated Press. "It's going to take people who are more independent to fix it. Arizonans value independence."
If Kelly is nominated the race would pit the Navy veteran and astronaut against McSally, a trailblazing Air Force pilot, in the contest to replace McCain, a legendary Navy flyer who was famously shot down and held captive in North Vietnam.
McSally is a former Republican congresswoman who was appointed to McCain's seat after she narrowly lost to Democrat Kyrsten Sinema last November in the race for outgoing Republican Jeff Flake's seat. McSally leaned heavily on her record as the first woman to fly a combat mission, but she was hurt by her embrace of President Donald Trump.
Kelly decried politicians who "ignore data and facts and in some cases don't even believe in science," but did not take on Trump directly, saying he's "not going to focus on the presidency or the White House."
The 2020 election will decide who finishes the last two years of McCain's term. The winner would have to run again for a full six-year term in 2022.
Democrats are eagerly watching the Arizona contest, having already defeated McSally. The party is also gauging whether Arizona could be competitive at the presidential level in 2020 after Trump won by 4 percentage points in 2016.
Kelly has never held elected office. He flew combat missions during the first Gulf War and was a Navy test pilot before becoming an astronaut along with his twin brother, Scott Kelly. He flew four space missions over 10 years and commanded the Space Shuttle Endeavor in 2011.
Kelly and Giffords have pushed Congress to enact gun control measures with little success. They shifted their focus to state legislatures in recent years, helping to strengthen background checks and domestic violence protections.
Giffords was severely wounded in a mass shooting on Jan. 8, 2011. The shooting at a Giffords meet-and-greet event in Tucson left six dead and 13 injured.
Giffords played a prominent role in the four-minute video Tuesday launching Kelly's campaign.
"I thought then that I had the risky job," Kelly says to Giffords. "Turned out, you were the one that had the risky job."
Kelly told the AP Giffords, who has been a rising Democratic star before the shooting, will join him frequently during campaign appearances.
Republican Gov. Doug Ducey appointed McSally to the vacant Senate seat after his temporary appointee, former Sen. Jon Kyl, resigned after a few months in office.
Arizona has been a longstanding Republican stronghold, but a growing Latino population and frustration among women with Trump have helped Democrats make inroads.
U.S. Rep. Ruben Gallego of Phoenix is also considering a Senate run that would likely position him to Kelly's left politically.
"I've made no secret of the fact that I'm looking seriously at running for the U.S. Senate in 2020, and that hasn't changed," Gallego said on Twitter following Kelly's announcement. "I'll be making a final decision and announcement soon."
Former Attorney General Grant Woods, a lifelong Republican who became a Democrat and a fierce critic of Trump, said last week he will not run for the seat.
McCain, a legendary and beloved Arizona politician, died last year from an aggressive form of brain cancer after more than three decades in the Senate.
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