Skating in the third-to-last pairing, Davis clocked 1:09.23. Mitch Whitmore was third at 1:09.32 to grab the third Olympic berth.
Davis is the world record-holder in the 1,000, and won the event at the 2006 and 2010 Olympics. He was eighth in Sochi, where the Americans were shut out of medals. Davis was an alternate on the 2002 Olympic team, but didn't compete in Salt Lake City.
"I look forward to going up," Davis said. "I know that there's some things I can correct. I think I can put myself in higher rankings worldwide."
On the women's side, Heather Bergsma won the 1,000, with Brittany Bowe finishing second to join her longtime rival on the Olympic team.
Bergsma was timed in 1:14.82 to make her third Olympic team. She has yet to win a medal.
"I'm happy to have the first one out of the way," she said. "It was a tough one, for sure."
Bowe was clocked in 1:15.52. The former college basketball point guard overcame walking pneumonia last fall during the World Cup season.
"A big relief," she said. "Nobody has an easy ride. Everybody has something going on."
Bergsma married Dutch speedskater Jorrit Bergsma in 2015 and relocated to the Netherlands, ending the training and roommate situation she and Bowe had shared.
"I definitely want to be back on that stage with her battling, a couple hundredths, tenths," Bowe said. "I don't like to see my time that far behind, but it is what it is. She's skating awesome. Hopefully we can both find ourselves on the podium in South Korea."
Mia Manganello finished third at 1:18.23, but because she hasn't met the Olympic qualifying time of 1:18.00, she cannot qualify to compete in South Korea. A U.S. Speedskating spokesman said the governing body's rules state an athlete must meet the time standard by the end of Olympic trials, which contradicted earlier information provided by Chris Needham, chairman of the organization's long track task force.
As a result, fourth-place finisher Jerica Tandiman will be nominated for the Olympic team, but won't necessarily skate the 1,000 in Pyeongchang. The U.S. is qualifying team spots for the Olympics and can determine who skates which events later.
Manganello missed qualifying in the 3,000 on Tuesday when she finished second. The U.S. only has one spot in that event for the Olympics.