The 26-year-old from Pennsylvania left it late and threw 21.93 metres in the fifth round to become the first American since 2009 to win the shot world title.
"It's the first team I made and being in U.S. shot put, you kind of expect to be at the top," Kovacs told reporters.
"It's my first world championships. Just coming here was just finding a few things. I dealt with it in different ways. I was excited to come away with the win."
Storl, the 2011 and 2013 world champion, had a best throw of 21.74, while the bronze medal went to Jamaica's O'Dayne Richards, who equalled his national record of 21.69.
It was a high quality final, with New Zealand's Tomas Walsh setting an Oceania regional record 21.58 in fourth place, and fifth placed Reese Hoffa, the 2007 world champion, throwing 21.00.
The third American to qualify for the final, Christian Cantwell, a 2009 world champion, was forced to withdraw on medical grounds, unable to compete after suffering a muscle spasm in his back following the morning's qualifying competition.
Kovacs came to Beijing at the top of the 2015 world rankings, having thrown22.56m in Monaco last month, the best effort in more than a decade.
The U.S. national champion quickly imposed his authority on the final with a first effort 21.23 but the German lay down his challenge by taking the competition lead with 21.46 in round two.
In the third round, Richards unleashed his best throw, the Pan-American champion giving himself the advantage of throwing last in the final three rounds.
It was Walsh who made the big move in the fourth round, hurling himself into the silver medal position.
But it was in the fifth round that the medal positions were determined, as Kovacs grabbed the lead with his best effort, punching the air in delight. Storl, next in the circle, responded with his 21.74 to take back second place.
(Writing by Steven Downes, Editing by Karolos Grohmann)
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