The UK's largest arena operator SMG was chosen in partnership with the largest international live entertainment company Live Nation.
The decision was announced by Bristol Mayor George Ferguson at a meeting of the council's cabinet earlier.
Bristol Arena, a 12,000-seat music venue, will be located at the Temple Quarter Enterprise Zone.
The arena is part of the city's plan to regenerate about 70 hectares (170 acres) surrounding Bristol Temple Meads station and is due to open in 2017.
The winning bidders will be involved in the design of the arena and in charge of operating, maintaining and managing it for the duration of the 25-year lease.
Mr Ferguson said: "SMG and Live Nation will bring the combined expertise of two global businesses in delivering an extremely exciting programme of concerts."
West of England Local Enterprise Partnership (LEP) will contribute £53m towards the cost of building the arena, with the remaining £38m funded by Bristol City Council.
Colin Skellett, of the LEP, said: "This is a project that Bristol desperately needs, it's been talked about for so long, and we will make it work between us."
Two companies have been announced as the combined preferred bidder to operate a £91m arena in Bristol.