The 15-year-old from Plymouth finished with 539.85 points to eclipse China's Qui Bo and Zhou Lukin at the Foro Italico after entering the final round in third.
It is the first world diving medal Britain has won since Peter Waterfield and Leon Taylor came second in the 10m synchro in 2005.
Daley said: "I don't know what to say.
"I don't believe it, I just don't believe it.
"Today was never the day when I thought I would become world champion.
"I woke up and thought just go out and enjoy it.
"To come away with a gold medal was unthinkable.
"It still hasn't sunk in.
"It makes all the sacrifices worthwhile.
"Now I want to do it again in London in the] 2012 [Olympics].
Daley received three perfect 10s and three 9.5s for his final dive, barely rippling the water as he sliced through.
But Daley's dives have a lower tariff - degree of difficulty - than his rivals which meant he was relying on them to make mistakes even if he was to execute perfect dives.
However, going into that final round, Zhou failed to make up the 10-point deficit and Daley clinched the bronze with a dive that earned him four 10s and was greeted with a beaming smile.
Olympic champion Matthew Mitcham was next to go but a poor execution cost him, giving the Briton the silver.
Qui - who beat Daley to the world junior title last year - had appeared in pole position to take the crown but an apparently nervous dive saw him earn points ranging from just six up to 8.5.
His attempt was greeted with gasps from the crowd who were aware Daley might actually have clinched the title and when the final scores came up with Qui 7.65 adrift of the Briton, there were celebrations in the stands from the British team.
Daley's father Rob was clearly overcome and the pair embraced.
Rob said: "It was a brilliant feeling when he was fourth.
"Then when he got bronze it was amazing.
"When he got silver I thought, 'I don't let it stop'.
"Then waiting for the last score when the Chinese man dived seemed like an eternity.
"I had a flashback of his life and I looked up and thought he's a world champion and he's 15.
"It's an unbelievable feeling."
Daley was tenth to dive in the competition and was first after the opening round but despite executing his second dive - a forward three and a half somersault in the pike position - he dropped to fourth behind Qiu, Mitcham and Zhou.
He remained there after the following round, just 0.35 behind Zhou with Mitcham leapfrogging Qiu into first.
Daley, diving immediately after Zhou, executed his fourth-round dive well but his lower degree of difficulty was counting against him and although still in fourth, Zhou was pulling away.
Qiu then reclaimed first from Mitcham as the pair fought their own private battle.
Zhou then had a poor entry on his penultimate dive in which he turned which saw him marked as low as 6.5 to offer a glimmer of hope to the Briton.
Daley took full advantage with a three and half back somersault which saw him awarded four 10s and into bronze position and with second-placed Mitcham in his sights with one round remaining.
Then came the drama of the final round with Daley excelling with his reverse three and a half somersault tuck and his rivals crumbling to leave the youngster on top of the world.
He said: "I was going to come fourth and I would have been really happy with that because it's great.
"But then to come away with a medal was great and then a gold medal was just insane, insane.
"At 2012 I really hope to do this again because the feeling I have got right now is incredible.
"I just want it to carry on."
Of the final two rounds, which saw him awarded a total of eight 10s, Daley said: "Those two are my favourite dives and that is why I leave them until last because I know under pressure I can do them well.
"I really thought they were going to catch up because they only needed seven and a halves and eights and for them not to get it is just crazy.''