More than 72 percent of the 37,535 votes went in favour of the project, however there was an extremely low turnout of just 31.65 percent of those eligible to vote.
"More than two third of the members have voted yes to the project of a new stadium and I want to thank all the members who have exercised their right to vote," said the club's president Josep Maria Bartomeu.
"We have proposed this project thinking about the future and the next generation of Barcelona fans."
The result is a victory for Barcelona's embattled board, led by Bartomeu, after a series of scandals that have hit the club over the past few months.
Sandro Rosell was forced to stand down as president in January after facing legal action over the controversial signing of Brazilian star Neymar, which saw the club charged with tax fraud.
And , Barcelona were handed a ban on signing players for two transfer windows by FIFA for breaching rules regarding the signing of players under the age of 18.
However, Bartomeu insisted that his message that the vote was more important to the future of the club than his succession of Rosell as president had been successfully received by the members.
"The project is for the club's future over the next 50 years. This is a club proposal, not one tied to this board. That is what we have said all along and I think the members have understood that."
The plans for the new stadium and surrounding areas include putting a roof on Europe's largest football stadium and increasing its capacity further from 99,000 to 105,000, as well as building a new multi-purpose indoor arena, a new stadium for the Barca B team, office and parking facilities.
Part of the funding for the project will come from selling a title right that will see a commercial sponsor's name added to the Camp Nou.
The club insist that supporters will be able to enjoy a significantly more comfortable matchday experience than is possible in the nearly 60-year-old stadium.
However, they also hope a drastic improvement to their hospitality services will create greater income for the world's second richest club.