He said: "Special circumstances exist that outweigh any harm to the green belt and other interests caused by the development."
The university first put forward plans for the 4500 m2 Centre for Behavioural Neuroscience in 1998. The application was twice turned down by South Cambridgeshire council.
A public inquiry was held last January and the government planning inspector agreed that the proposed building would harm the green belt. He also noted that protests over vivisection carried out by animal rights campaigners could lead to severe traffic disruption.
The university must now raise an extra £8m for the scheme because costs have risen, partly as a result of stricter rules governing the use of laboratory animals.