In a statement, the 58-year-old Mr Kelly, the incumbent senator, said: “Thank you to the people of Arizona for re-electing me to the United States Senate.
“From day one, this campaign has been about the many Arizonans – Democrats, Independents, and Republicans – who believe in working together to tackle the significant challenges we face.
“That’s exactly what I’ve done in my first two years in office and what I will continue to do for as long as I’m there. Democrat Mark Kelly wins in Arizona senate
“It’s been one of the great honours of my life to serve as Arizona’s senator.
Democrat Mark Kelly wins in Arizona senate
“I’m humbled by the trust our state has placed in me to continue this work.”
Mr Kelly is a former US Navy captain and retired astronaut who made four trips into space, including missions delivering equipment, supplies and crew to the International Space Station.
If Mr Kelly’s victory leaves the senate tied at 49-49, with control hinging on contests in Nevada and Georgia.
The Democrats need one more seat, as Democrat Vice President Kamala Harris can cast a tie-breaking vote.
In Nevada, incumbent Democrat Catherine Cortez Masto is within 800 votes of the Republican state attorney general Adam Laxalt.
The outcome in Georgia could be weeks away, with Democrat incumbent Raphael Warnock to face Republican Herschel Walker in a 6 December run-off.