The 31-year-old German won his first world title on Sunday, beating Mercedes team-mate Lewis Hamilton by finishing second in the final race in Abu Dhabi.
"I have climbed my mountain, I am on the peak, so this feels right," Rosberg said in a Facebook post.
Rosberg won nine of this season's 21 grands prix, beating three-time champion Hamilton by five points.
"For 25 years in racing, it has been my dream, my 'one thing' to become Formula 1 world champion," he added.
"Through the hard work, the pain, the sacrifices, this has been my target. And now I've made it."
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That's fast