The design will feature a moveable flying saucer-shaped roof covering the central arena, allowing the space to be used for open-air and indoor events.
"It's like a UFO has been dropped onto the site," said Wise.
The project will also feature an 80 m tower and an underground multiplex cinema with a link to a metro station.
The Les Arenes bullring is one of two in the city. It was built in 1929 to coincide with Barcelona's world fair.