Gidey, the world record holder over the distance, hit the last 400m of the 25-lap race at Eugene's Hayward Field in complete control and crossed the line in a winning time of 30min 09.54sec.
"This was the biggest aim I had," Gidey said. "The dream came true. This victory is even more important to me than a world record, I am so happy about this performance.
"I was thinking about winning this gold since 2019. But Hassan was always there. I was also watching Obiri."
Gidey added: "This time, I was really watching them and I knew I had to be very fast in the last 300m. I managed to stay in front and kept the pace until the finish line.
"I have the next dream now - to win the gold at 5000m... I am very confident now."
Kenya's Hellen Obiri took silver in 30:10.02, with her teammate Margaret Chelimo Kipkemboi claiming bronze, just ahead of defending champion and Olympic gold medallist Hassan.