American Mac Forehand took silver, Matej Svancer of Austria earned bronze and Ruud was left empty-handed in the event, which took place under sometimes challenging conditions due to heavy snow at the Livigno alpine resort.
With the best two scores out of three jumps deciding the winner, Frostad wowed the judges with a near-perfect 195.5 out of 200. Forehand and Svancer posted 193.25 and 191.25 respectively.
At Beijing 2022, the top three posted far lower scores, with Ruud getting 187.75 and the other two medallists 183 and 181.
"Shout out to everyone," Frostad told reporters. "We all did amazing, even though the conditions were quite challenging, it ended up being, like, probably one of the greatest events ever."
Winner sips prosecco
It was the first Olympic podium for 23-year-old Frostad, who was fourth in Sunday's qualifiers and 12th in last week's slopestyle final. He stands 18th in the overall World Cup rankings.
Frostad celebrated with the Norwegian flag wrapped around his shoulders, sipping from a bottle of Italian prosecco sparkling wine.
Forehand, 24, came into the final in hot form after topping the qualifying round and with a big air win at the X Games in January. He said, with a big grin, that he was now looking forward to a surfing holiday in Mexico.
Svancer, another first-time Olympic medallist who excelled in the qualifiers with a second-place performance, offered to join him - as did Frostad.
Ruud, meanwhile, leaves Milano Cortina with a gold in slopestyle to adding to his big air title from 2022.
On Tuesday he posted a high score of 95 in the first run, but fluffed the next two.
In big air, skiers jump off a steep ramp, sometimes backwards, and perform as many flips and turns as they can, before landing as cleanly as possible, at speeds of over 60 kph. Judges assess height, technique, originality and other factors.
It is a high-risk discipline that can easily result in injury. In Sunday's qualifiers, Finland's Elias Lajunen had to be carried away on a stretcher and taken to hospital after crashing awkwardly on his back.