The arena will be built on a site across from the 99,354-seat football stadium to become the home of professional basketball team FC Barcelona Lassa.
The main court will have seating located as close to the edge as possible to offer spectators a clear view of the action.
Two "sky bars" and 18 VIP spectator boxes will occupy an upper level above banks of seating.
Other elements of the HOK-designed scheme include an auxiliary court capable of hosting 2,000 spectators and an ice rink.
The New Palau Blaugrana arena is part of a wider redevelopment plan for a site that is currently occupied by the Mini Estadi – a 15,276-seat stadium. The development will link the area to FC Barcelona's football school.
"Our design creates an organic building geometry that supports a seamless progression between the New Palau, the annex court, the ice rink and the FCB Escola academy training facilities," said John Rhodes, a director of HOK's Sports + Recreation + Entertainment division. "We're excited about the benefits that this project will bring to FC Barcelona and to this cosmopolitan city."
A jury that included members of the FC Barcelona sports club selected the scheme from 19 other entries and praised it for its "permeability, flexibility and personality".
The complex is expected to be complete in time for the 2019-2020 Euroleague basketball season.
The Camp Nou, which was built in 1954, is a key fixture in Barcelona's skyline. Antoni Gaudi's Sagrada Família basilica – the city's most famous landmark – is located to the northeast of the stadium site and recently hit the headlines after it was announced that construction work on the cathedral had entered its final stage.
Other recently unveiled designs for sports stadia include Herzog & de Meuron's revamp of Chelsea FC's London stadium and an elliptical proposal by Populous for rival London football club, Tottenham Hotspur.