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.
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."
The son of Finland's 1982 world champion Keke, Rosberg made his F1 debut for Williams at the Bahrain Grand Prix in 2006, finishing seventh.
Mercedes team boss Toto Wolff said the news took him "completely by surprise".
"This is a brave decision by Nico and a testament to the strength of his character," he added.
"The clarity of his judgement meant I accepted his decision straight away when he told me.We now have to consider options and we will start to look at it on Monday."
Rosberg raced in 206 grands prix winning 23 and finishing on the podium 57 times.