Populous, who designed the London Olympic Stadium and the O2 arenas in London, Berlin and Dublin, was chosen from a shortlist of five.
Bristol Arena, a 12,000-seat venue set to open in 2017, will be built in the Temple Quarter enterprise zone.
The council said more than 50,000 people viewed the five designs online and it had received about 550 comments.
The judging panel, which included the mayor, Bristol City Council and the Royal Institute of British Architects, said it "took the comments fully into consideration when scoring the designs".
Populous was praised by the panel for its "unique innovative concept that allows for smaller capacity theatre style events, while quickly converting to larger configurations for sporting events, major conventions or exhibitions".
Mayor George Ferguson said: "The Populous team has presented an innovative design for a horseshoe-shaped arena that will allow us real flexibility for programming, for now and into the future".
Nicholas Reynolds, from Populous said: "We believe Bristol Arena will be the catalyst for the creation of a vibrant new quarter in the city."
The project is funded by the city council and the West of England Local Enterprise Partnership, through its Economic Development Fund.
The council said it expected to "break even within ten years" and hoped the arena would "bring some of the greatest acts and events as well as millions of pounds of economic growth to the region".
The arena is set to be located on the former diesel depot site next to Bristol Temple Meads railway station, in the Bristol Temple Quarter Enterprise Zone.
The winning team to design a £91m entertainment arena in Bristol has been announced.