The energy company will deliver smart energy propositions, such as local tariffs and innovative services, designed to reduce carbon and peak power demand.
In return, it will benefit from external investment, significantly reducing its reliance on council funding.
Following the unveiling last year, the council said City Leap has attracted interest from more than 180 local, national and international organisations, including technology firms, investors, community groups as well as energy and infrastructure developers.
The procurement process will run for several months.
Mayor of Bristol Marvin Rees added: “City Leap is a world first. We are creating a decarbonised local energy system that Bristol can be proud of. City Leap is leading the way on carbon reduction, while at the same time addressing important social and economic challenges.
“The inclusion of Bristol Energy is integral to delivering smart energy propositions utilising City Leap’s projects by weaving a number of technologies together, helping to ensure that the company continues to deliver clean energy and social value for local people.”