The Faraday Lecture Block dates back to the 1960s and the university says its "tired and monotonous design" means it has become a bit of an eyesore.
As well as new multi-coloured external glass cladding, the building will have a new entrance hall, extended second floor and improved access.
Work on the 11-month project is due to start in January.
The university said the new look would add vibrancy to the building and the mall area.
The majority of construction will take place during the Easter holidays and summer months.
A spokeswoman said: "It'll create a good impression and reflect the standards that Swansea holds and a professional atmosphere that fits in with the degrees that are taught in that building".
One of the main buildings on Swansea University's Singleton Park campus is to undergo a £2.75m makeover.