The club's board of directors have confirmed they will instead redevelop the Nou Camp and the option of boosting the capacity from 98,000 to 105,000 will be voted on by Barca members in April.
The project, which also includes the construction of a new indoor basketball arena, is expected to cost around £495m, and would see a new roof added to the current structure.
Work would begin in 2017 and should be completed by early 2021 but matches would still be played there while the work is carried out.
"It was a difficult decision," said club president Sandro Rosell.
"The two projects were very attractive but we were committed to put to a referendum a project that was viable from a technical, urban-planning and economic perspective.
"The Nou Camp is part of our collective memory, the biggest stadium in Europe and an icon of the city of Barcelona.
"The option of building a new stadium on a new site has been rejected as the final cost could have saddled the club and its members with debt and tied the hands of future boards of directors."
The plans for the remodelled stadium, which opened in 1957, include the construction of a steeper bottom tier that would offer improved sightlines for supporters.
There would also be new restaurants with a view of the pitch and "super boxes".
"To maintain our status as leaders we have to take this historic step which will require effort from everyone involved," added Rosell.
"We will increase the value of our real estate and the capacity to generate additional income without having to sell off assets."