The Kentucky born Hayden became the first American to win the title since Kenny Roberts in 2000 when his third place gave him enough points to pass the Italian who had crashed on the fifth lap and could only recover to 13th place.
An overjoyed Hayden said it was a dream come true.
"I am just really, really proud, man!" said Hayden.
"You dedicate yourself to something for life and then it comes off. It is wonderful.
"We were really down after Portugal (he crashed giving Rossi the series lead for the first time) but this proves dreams really come true," said the 25 year old, whose family were present for the occasion.
Rossi admitted he was devastated by the defeat.
"It's a disaster," said the Italian.
"It's disappointing to have come to the last race with an eight point lead and not to win the title.
"I made two mistakes - a bad start and the fall, but that's racing. All I can say is 'bravo' to Nicky because he's a great rider.
Over and out for Rossi
"He's the champion because he was the best this year."
The race was won by Australian Troy Bayliss, his first victory at the top level as he too soaked up the emotion.
"It's been a crazy weekend," said Bayliss.
"It is more than a fairytale."
Just three months ago, Hayden had looked to be on course for a comfortable victory in the world championship after opening a 51 point advantage over Rossi who was in the third place at the time.
However the Italian fought back in stunning fashion to overtake Hayden after the last race in Estoril.
After a poor start which was exacerbated with a fifth lap tumble, Rossi was back in 20th place and despite his best efforts, Hayden was able to stay with the leaders and clinch his maiden title.
Plenty of flag waving on the victory
The American exploded with joy after the chequered flag and Rossi showed what a sportsman he is by riding alongside him on the victory lap and holding his hand.