According to the council plans, the arena and conference centre will be built adjacent to Temple Meads station and be completed by June 2017.
The council is expecting to borrow £53m from its City Deal and raise the remaining amount of £38m from the arena operator and car parking income.
The elected mayor of Bristol, George Ferguson, also supported the efforts to start the search for an arena operator and settling the terms of the lease with them.
The funding package for the arena will be handed over to the council on 18 February as part of the council’s budget proposals.
Upon the approval of the full council, the scheme’s total budget for the next three years will have to cover construction costs of £1m in year one, £25m in the following year and finally £65m in 2016/17.
However, Mr Ferguson stated that the net project costs would be in the region of "very low millions".
He added: “We know that there is a ready audience to come to Bristol to see performances and we know that there are operators keen to run the arena for us but we also know that arenas cannot be built without some public subsidy.”
Next month, the full council will have a discussion on the Mayor’s proposal to withdraw £83m from the city council's budget throughout the next three years, which will most certainly result in loss of up to 800 jobs, and cuts to library and children's centres funding.