In the exact sense, a tyrant is an individual who arrogates to himself the royal authority without having a right to it. This is how the Greeks understood the word 'tyrant': they applied it indifferently to good and bad princes whose authority was not legitimate. [Rousseau, "The Social Contract"]
The spelling with -t arose in Old French by analogy with present participle endings in -ant. Fem. form tyranness is recorded from 1590 (Spenser); cf. Medieval Latin tyrannissa (late 14c.).