The Guildhall, on the banks of the River Severn, and Rowley's House will both be used by the new University Centre Shrewsbury when it accepts its first students in September.
The Guildhall will be the main base for lectures, while Rowley's House, in Barker Street, will be used for administration and teaching.
The applications, which were both supported by Shropshire Council's planning officers, were approved by its central planning committee at Shirehall yesterday.
The plans for the 16th century Rowley's House – a former museum – will not alter its look, but simply allow the change of use.
Councillor Andrew Bannerman described the timber-framed building as a "prize asset to the town".
"The university has worked well with local people and the local council," he added.
A report prepared by council planning officers said: "It is considered that the proposed use of Rowley's House for education and administrative purposes is acceptable in principle in this sustainable location within Shrewsbury town centre."
Shropshire Council and Shrewsbury Town Council are based at the Guildhall, but most of Shropshire Council's workers and services have already moved out.
A report prepared by planning officers said: "The proposal includes no alterations to the building and would therefore have no adverse impact on the appearance of the building or local amenity."
University Centre Shrewsbury is being developed in the Frankwell area by Shropshire Council and the University of Chester.
They say it will be "unique, distinctive and will develop Shropshire's economy whilst also having significant national and international relevance".
Plans to convert Mardol House, which joins the market hall at the top of Mardol, between Shoplatch and Claremont Street, into living accommodation have already been approved.
The building will be transformed into nine self-catering flats with five or six en-suite bedrooms for 49 students, and studio apartments for another 36 students.
The development will transform the empty office block, and four of the studio apartments will be adapted for students with disabilities.
The council, which owns the freehold, submitted the application to convert part of the building into living quarters for the new University Centre Shrewsbury.