The Briton prevailed in a breathless, frenetic and wildly unpredictable US race - and with Mercedes team mate Nico Rosberg beating Ferrari's Sebastian Vettel to second, earned an unassailable lead in the standings.
"It's difficult to find the words really. I owe it all to my dad and family who supported me all these years and sacrificed so much," Hamilton said afterwards. "It's a very humbling experience, especially to equal Ayrton Senna [on three world titles] - I feel very blessed today.
"It's the greatest moment of my life. I pushed and pushed - I hope I can inspire people to never give up. It's just crazy to think I'm now a three-time world champion."
Hamilton admitted there were several occasions where he thought his chance of victory was over, particularly after dropping to fourth at mid-distance and then losing the advantage to Rosberg late on.
"Today so many times I thought I had lost the race," he said. "Nico was really quick in stages, he pitted under the Virtual Safety Car…but never for one second did I think I couldn't do it.
"I'm buzzing inside… I can't find the right words to express the feeling but it's the greatest I've had in my life. Nico drove a fantastic race, mad respect for him as a team mate. I just can't believe I'm sitting here. To my family, I love you. To the team, thank you so much - I'm overdue a drink with the team!"