There have been no recorded cases of yellow fever in the country’s tourist regions (most of the country, really) in the last twenty years. However, when planning to visit the less visited parts, it may be recommended that you get a yellow fever vaccination two weeks before your planned travel date. This vaccination is effective for ten years.
The problem of malaria in Tanzania is greatly exaggerated. Not all species of mosquito carry malaria to begin with, and contracting malaria is unlikely in most parts of the country. But just carry a mosquito repellent for your safari or you may get one on arrival. Prior communication required.