The 23-year-old set three personal bests in the final and his longest throw of 22.52 metres shattered an Olympic record set by East Germany's Ulf Timmermann in 1988.
Crouser's victory, which followed Michelle Carter's last-gasp win in the women's shot put, took the United States back to the top of the men's podium in an Olympic event the country has dominated with 18 of the 28 gold medallists.
Crouser stunned his rivals to win the U.S. Olympic trials and during the Games final he looked untouchable. He was the only man to throw over 22 metres, which he did three times.
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"It's an amazing experience (to win in front of my family). I can't even describe it," Crouser said.
His compatriot and reigning world champion Joe Kovacs had to settle for second with a best throw of 21.78m.
"You're never happy getting second," said Kovacs, who secured the Americans first one-two finish in the event since 1996.
"But it's settling in now that I'm still bringing home the silver medal for the United States and the gold is coming home with Ryan."
Tomas Walsh grabbed bronze to win New Zealand's first male shot put medal at the Olympics.
"It's pretty cool isn't it," Walsh said. "It was awesome to be out there and to have a Brazilian in the field and the crowd going nuts; it was an awesome atmosphere."
Poland's 2008 and 2012 Olympic champion Tomasz Majewski finished sixth after an error-strewn performance in which he recorded only two legal throws in six attempts.
New Zealand's Jacko Gill, 21, defied doctor's orders to put in a gutsy performance with a stress fracture in his foot, but had to settle for ninth.
(Reporting by Drazen Jorgic; Editing by Ed Osmond/Greg Stutchbury)
