The 26-year-old became Britain's first champion since Tom Simpson won gold in 1965.
"It was incredible, we took it on from start to finish," said Cavendish.
"I can't believe it. We knew three years ago when this course was announced - we put a plan together to put these best guys together.
"It's been three years in the making and you just saw they rode incredibly. I'm just so proud."
The victory capped a successful year for the Manxman, who won the Tour de France green jersey at the end of July.