The 24-year-old finished just 0.04 seconds behind friend and team-mate Tom Dean, who produced a British record on his debut Olympic appearance to finish in 1m 44.22s.
Fernando Scheffer of Brazil took bronze.
Scott was the hot favourite going into the final but after the race said he was "buzzing” for his friend and team-mate.
"He has come on so far in the last 18 months – it is a pleasure to watch," Scott said.
“He’s a good mate out of the pool and it’s great to be able to compete against him."
The success is all the more remarkable considering Dean twice contracted coronavirus in 2020.
Speaking to BBC Sport he said he could scarcely believe how far he has come since the days he struggled to climb stairs without coughing and wheezing.
"When I was sitting in my flat in isolation, an Olympic gold seemed a million miles off. It is a real honour.
"I watched the flag go up and the anthems be played… it’s the stuff of dreams."
The 21-year-old was twice forced to take time out which he feared could dash his Olympic hopes.
"The three week build-up back to training had to be structured to prevent any long-term damage to my heart and lungs – it was scary," he added.
"It was upsetting – no-one takes six weeks off in the build-up to an Olympics. It was a real shock to the system."
Dean's gold is Britain's fourth of the Games after Adam Peaty, Tom Pidcock, and Matt Lee and Tom Daly’s triumphs on “Magic Monday”.
Elsewhere, Scotland’s Kathleen Dawson finished sixth in the 100m backstroke final with Australia's Kaylee McKeown winning gold, Kylie Masse of Canada coming second, and Regan Smith of the United States of America taking the bronze medal.
Freya Anderson missed out on qualifying for the 200m freestyle final while Team GB’s Abbie Wood and Alicia Wilson both qualified for the 200m individual medley final after finishing second and eighth respectively.
Their final will take place at 3.45am BST on Wednesday.