He came close to victory during the 2021 Russian Grand Prix but lost the lead with four laps to go after being caught out by a late rain shower.
In Miami, he showed good pace all weekend in a McLaren that featured several upgrades.
“What a race. It’s been a long time coming but finally I’ve been able to do it,” he added.
“I’m just proud really. I mean, a lot of people doubted me along the way.
“I’ve made a lot of mistakes over the last five years, my short career, but today we put it all together so this is all for the team.”
It is McLaren’s first victory since the 2021 Italian Grand Prix when Daniel Ricciardo took the win ahead of Norris.
Three-time world champion Verstappen, who has won four times while dominating the season so far, finished nearly eight seconds behind Norris and said the Briton was “flying”.
He added: “I’m very happy for Lando. It’s not going be his last one. He definitely deserves it today.”