The 18-year-old was narrowly beaten by the US's David Boudia, who won gold, and China's Qiu Bo, who takes home the silver. He earned a total of 556.95 points, and was watched by One Direction and David Beckham at the Aquatics Centre.
Daley's medal placing comes after just missing the podium during the men's synchronised 10m platform on July 30, placing fourth with diving partner Peter Waterfield.
The teenager has been congratulated by fellow sports stars, politicians and celebrities on Twitter - Digital Spy collects a selection of their reactions:
Phillip Schofield: "Well done @tomdaley1994 incredibly high scoring night and a brilliant bronze. We're all so proud and your Dad would be bursting with pride."
Lemar: "Congratulations Tom Daley! #TeamGB."
David Lammy MP: "Probably no more TeamGB athlete under more pressure to perform than Tom Daley. Got to give it to him.#daley#diving#olympics."
Ed Sheeran: "Yes @TomDaley1994 !!!!!"
Joey Barton: "Made up for Tom Daley getting a medal there. It's been a hard old couple of years for him. His father would be proud."
Russell Brand: "I'm going to wait for Tom Daley in the little pool he goes in after he dives and cuddle him too hard."
Coleen Rooney: "Congratulations Tom Daley!! That was fantastic!!!"
Conor Maynard: "Can't watch the diving cuz I'm stuck in some airport... but seeing a running commentary on my timeline! :) YES @TomDaley1994 !!! #DidUsProud"
Chris Moyles: "Well Done @TomDaley1994!! Amazing!!"
Little Mix: "congratulations to @TomDaley1994 he's done us proud! #TeamGB xxjadexx"
Austin Healey: "Well done @TomDaley1994 made a nation proud."
Caroline Flack: "Love a diving montage!! Well done @TomDaley1994."
Arlene Phillips: "@KennyLogan: Well done @TomDaley1994 you've done your dad so proud. Super star." Joy to behold."
Steps' Claire Richards: "Well done Tom Daley!! Sooo exciting to watch and so proud of another british medal x"
Danny Cipriani: "So happy for Tom Daley... Good guy, great talent!"
Frankie Cocozza: "massive congratulations to @TomDaley1994."
Rosie Huntington-Whiteley: "@TomDaley1994 one word...AMAZING!"
Kimberley Walsh: "What an amazing competition! Congrats @TomDaley1994 #GoTom #Olympics2012 #OurGreatestTeam."
Cheryl Cole: "Congratulations @TomDaley1994.. You did us all proud.. !! Now you should have some free time to teach me that dive !! :D"
Derren Brown: "Congratulations @TomDaley1994 just heard the news!"
London 2012 Olympics rolling gallery:
Copyright: Martin Rickett/PA Wire/Press Association Images