That depends mostly of the period you are dealing with. Octavian became "emperor" mainly due to exceptionnal powers that was given by the roman senate: proconsular power in the "imperial provinces" (where all the legions minus one were garrisoned) and the power of the tribune of the plebs without being a tribune...All these powers were sanctionned by the senate. Every new emperor was supposed to be granted those powers by the senate, the "lex de imperio vespasiani" is the law allowing the imperial powers to Vespasian. The importance of the senarorial law was in reality almost inexistant as it only sanctioned the heir chosen by the current emperor or by the army. I don't really know details about the IIIrd century as multiple civil wars create a challenge to the question of legitimity. I would be happy if someone could add something about the legislative base of the tetrarchy, and if laws that look like the lex the imperio vespasiani were still made in the IVth century.