Proposals in the application include seven new buildings on the former Royal Mail sorting office site and part of Arena Island, close to Bristol Temple Meads railway station.
A separate part of the Arena Island site is earmarked for the long-delayed Bristol Arena scheme.
According to the university, the new buildings would provide flexible research and teaching facilities, accommodation for up to 1,500 students, and a range of commercial outlets.
The campus would also house a "Quantum Technologies Innovation Centre", designed to help businesses harness the power of atomic and subatomic matter and energy.
The campus would initially cater for 3,500 students, largely postgraduates, and about 800 members of staff.
University of Bristol president Hugh Brady said: "Not only does the project build on Bristol’s reputation as one of the world's leading digital cities, but it’s injecting life into a derelict site and creating unprecedented opportunities for our students and the community we’re so proud to be part of."
The university said that work is expected to start on site in mid-2019, with the first phase of the campus open by autumn 2021.