The 31-year-old German, who beat off teammate Lewis Hamilton in the finale, is the first reigning champion to quit since Alain Prost in 1993.
Rosberg made the bombshell revelation in Vienna ahead of the International Automobile Federation (FIA) annual awards ceremony.
"I have decided to end my Formula One career here," said Rosberg, who claimed the title at the Abu Dhabi Grand Prix on Sunday when he came second to Hamilton.
He said he made the decision in the aftermath of his championship triumph. "It was a process on Monday," Rosberg added.
"I didn't know if I had the balls, and I took a bit of time. "But I am done. End of story and the next step is being a dad and a husband and I am very much looking forward to that."
Mercedes team boss Toto Wolff said: "For the team, this is an unexpected situation and an exciting one."
Wolff hailed the achievements of Rosberg. "This is a brave decision by Nico and testament to the strength of his character.
"He has chosen to leave at the pinnacle of his career, as world champion, having achieved his childhood dream."
Wolff said Rosberg's "relentless" drive and "inspirational way" of fighting adversity, mixed with his "tenacity and grace under pressure" had earned him "the respect of the sport".
In capturing the title Rosberg emulated his father Keke who won the F1 crown in 1982. Rosberg began karting aged six.
He and Hamilton met as rivals in 1997 and became team-mates in 2000. In 2002, he moved to the German Formula BMW championship and won the title.
Rosberg arrived in F1, with Williams, via the Formula 3 Euro Series and winning the inaugural GP2 title in 2005.
Before joining Williams, he turned down a place at Imperial College, London, to study aeronautical engineering.
Rosberg claimed his first podium at the 2008 Australian Grand Prix, sharing the moment with a victorious Hamilton who had arrived in F1 with McLaren a year earlier.
In 2010, he moved to the rebranded Mercedes team created by the German manufacturer's takeover of the 2009 champions Brawn.
He recorded consistent finishes as team-mate to returning Michael Schumacher before the seven-time champion's final retirement and the arrival, in 2013, of Hamilton.
Their partnership ignited the team's spell of dominance. Though Hamilton beat him to be champion in 2014 and 2015, the methodical Rosberg finally took the crown in 2016.
Rosberg takes his leave of Formula One with 23 race wins and 30 pole positions. He is now relinquishing life in the fast lane to spend time with his wife, his childhood sweetheart Vivian Sibold with whom he has a daughter, Alaia, born in August last year.
He posted a message to his fans on social media, saying "I have a message for you". "Since 25 years in racing it has been my dream, my 'one thing' to become Formula One World Champion.
"Through the hard work, the pain, the sacrifices, this has been my target. "And now I've made it. I have climbed the mountain, I am on the peak, so this feels right." Wolff said Rosberg's exit presented Mercedes with "an unexpected but exciting situation".
"We are going into a new era of technical regulations and there is a free Mercedes cockpit for the seasons ahead."