More than 55 percent of the votes came in favour of holding the games, compared to 44.9 against.
"This is a huge relief. Thank you to everyone who has made the dream live on. Thanks to everyone who voted 'yes'" said Børre Rognlien, President of the Norwegian Sports Federation.
The vote took place at the same time as Norway's general election, with Oslo citizens asked to also vote on the city's Olympic plans.
As recently as August 21, a poll conducted by research agency Norstat showed that as many as 57 percent of Oslo residents were against holding the games.
The city is now free to make its application to host the games before the 14 November deadline, with tough competition expected from Munich, Stockholm, Barcelona, and Sarajevo.