His gong takes Team GB’s total Winter Olympic medal haul to a record five – surpassing the four won in Chamonix in 1924 and in Sochi in 2014.
The 28-year-old snowboarder, from Southampton, joins Lizzy Yarnold, who won gold in the skeleton, Laura Deas and Dom Parsons, who both won bronze in the skeleton and Izzy Atkin who won bronze in the ski slopestyle.
There were scenes of jubilation as Morgan realised he had secured a medal in big air, which involves pulling off the most impressive airborne trick possible after jumping off a giant ramp.
He had only just squeezed into the final 12 in the event and scored 168 with his two jumps but was aided by the failure of some of his rivals to successfully land twice.
Morgan’s third place was behind gold medallist Sebastien Toutant of Canada and Kyle Mack of the United States, who claimed silver.
He was only 6.25 points behind Toutant and 0.75 behind Mack.
The event was watched by Donald Trump’s daughter Ivanka, who cheered on her second-placed compatriot.
The big air event was making its Olympic debut in South Korea, with Austrian Anna Gasser winning the women’s gold medal on Thursday.
Team GB, who are currently 18th in the medal table, had set themselves the target of achieving five medals.
Minister for Sport Tracey Crouch said it had been a ‘fantastic two weeks for British winter sport’ and congratulated the team on their achievement .
“The performances of our athletes have made the country proud and been an inspiration to many back home.” she added.
There is still a chance of at least one more medal if the women curlers are able to take bronze in the playoff for third after the team lost to Sweden in the semi final on Friday.
Morgan didn’t take up snowboarding until he was 17 and only embarked on his first full winter on snow at 17.
In January 2012, a video of his performing a snowboarding trick attracted more than one million YouTube views.
More from UK
Stormzy tweets ‘job done’ after Grenfell Tower fire petition reaches 100,000 signatures
Beauty Banks: The toiletry equivalent to food banks takes off
Check your numbers: UK EuroMillions player wins nearly £78m
Moments before fatal Coventry hit-and-run caught on CCTV
James Brokenshire calls for end to lung cancer stigma as he confirms he has been treated for disease
EU boss Donald Tusk claims UK’s Brexit plans ‘based on pure illusion’
He is a social media star for his stunts, which include being the first to perform four flips and five full rotations.
But he is no stranger to conventional media either, having posed wearing just his snowboard boots and his board for a national newspaper feature ahead of the Games.