The couple, who won silver at Vancouver 2010, led all the way to seal the title by 4.53 points following a routine filled with difficult lifts and rapid footwork, that placed them ahead of defending Olympic champions Tessa Virtue and Scott Moir of Canada. Russia's Elena Ilinykh and Nikita Katsalapov won bronze.
“We're so excited, we're in shock a little. I'm not sure what we're feeling,” said Davis, after he and White became the first ever US skaters to win gold in the ice dance.
“It kind of all came together for us and we're so pleased to be here. We're in disbelief.”
The Americans, who train with the Canadian silver medallists Moir and Virtue under Russian-born coach Marina Zoueva, scored 116.63 points for their free skate to "Scheherazade".
That was more than two points higher than the previous world record, which they had set just over a week earlier in the team event.
Having already set a world record in the short dance, their combined total of 195.52 also represented a new benchmark, beating their previous best, set at the Grand Prix final, by over four points.
“The crowd was really alive out there today for all the teams and we fed off the energy,” said White, before paying tribute to their coach. “We were well prepared by our coach Marina (Zoueva) in coming here and doing our job.”
“I felt like we had done everything we could from the beginning of this competition, in practice, team event, this event. And 17 years of hard work was justified. To come away with a gold medal is amazing.”
The Canadian pair scored 114.66 points for their skate to "Petit Adagio, Waltz in Concerto No. 2" for an overall total of 190.99. It was a further personal triumph for Zoueva, who inspired Moir and Virtue to gold four years ago.
“That was another great skate for us,” said Moir. "There was a lot of pressure tonight. We felt it more this afternoon probably than yesterday.
“We just wanted to go out and have a great skate for us and have our moment and we felt like we did that,” he added.
Virtue and Moir became the first Canadians to win three Olympic medals in figure skating, adding two silvers won in Sochi to their gold from Vancouver 2010.
“With more experience comes more pressure, more expectation,” added Virtue. “I think in Vancouver we maybe had the benefit of not knowing what the Olympics are really all about and having not experienced it, but I think coming in we knew exactly the magnitude and the scope of it.”
Ilinykh and Katasalapov, who came into the ice dance competition having won gold in the new team event, scored 110.44 for an emotionally charged performance to "Swan Lake", which earned a standing ovation, and helped them to an overall score of 183.48.
The bronze for Ilinykh and Katasalapov meant a sixth consecutive Olympic podium for Russian dancers in the event.
It was also just the fourth time that the gold had gone to a couple from outside Russia or the former Soviet Union since ice dance made its Olympic debut in Innsbruck in 1976.