The club says 37,535 of its 118,580 eligible members participated in the referendum, with 72 percent voting yes.
Members voted at the stadium on Saturday, when Barcelona beat Real Betis 3-1.
Built in 1957 and enlarged in 1982, Camp Nou holds 98,000. The plan is to increase that to 105,000.
The approved project includes the construction of a new sports pavilion for the club's basketball, handball, indoor football and roller hockey teams.
