In Arena and Daggerfall, it was simply known that he was human, as the Imperial race didn't necessarily exist back then. In Oblivion, his in-game race is Imperial.
Tiber Septim's race isn't necessarily relevant. Whatever it was, his and his brother's heirs have had their bloodlines mixed with multiple races. Take Pelagius Septim III for example; he was part Altmer. Septim was human, though it is unknown which specific race. In Letters to The Elder Scrolls Adventures it is stated he is Atmoran, not Nord. This is likely the Orthodox version however, basing it off that he is from Atmora. The Heresy claims he was a Breton from Alcaire, High Rock.