The German finally ended his long wait to become a Formula One drivers' champion on Sunday when his second-placed finish behind Hamilton at the Abu Dhabi Grand Prix was enough to pip his rival by five points at the top of the standings.
It ended Hamilton's two-year winning streak in the championship, although the Briton did all he could to claim his fourth world title by driving slowly at the Yas Marina circuit in an attempt to get rivals to overtake Rosberg.
Rosberg refused to discuss Hamilton's tactics and instead used his first press conference as world champion to praise him.
He said: "I owe some words to Lewis. He's one of the best in the world, one of the best ever surely, so it's incredibly intense to race him.
"I've got great respect for him because he does an incredible job, he's done so well over the years and he fought to the very last metre on Sunday. "That made it extremely tough on Sunday but all the more beautiful afterwards."
The pair were good friends as children when they started go-karting together, but Rosberg admitted their tense rivalry has eroded that friendship in recent years.
"It will always be difficult between us. We are in the same team and race against each other for titles," he added.
"It is virtually impossible to have a good relationship. We used to be best friends when we were young so at least we have this respect for each other. This helps somewhat."