I don't know of any official size. Personally, I like to think Daggerfall is actual-size, and the later games are all scaled down, but with all the dragon-breaking and CHIM that goes on in TES, the true size of Tamriel is probably just whatever you want it to be.
In the manual that came with Arena, Tamriel was stated to be roughly 4000 by 3000 kilometers, which makes its area 12,000,000 square kilometers. This makes it a bit larger than Europe.
In Daggerfall, the Illiac Bay region was scaled as roughly 161,600 square kilometers according to wikipedia.