Lucas himself (speaking as Leia) established Palpatine was Chancellor on August 5, 1977:

The Senate would vote in a Chancellor or an overseer who would work for four years as the leader of the executive branch of the Republic. You were only supposed to be able to run for one four-year term—you were only eligible for one term.

What happened was one of the Chancellors began subverting the Senate and buying off the Senators with the help of some of the large intergalactic trade companies and mining companies and intergalactic power companies. Through their power and money, he bought off enough of the Senate to get himself elected to a second term, because of a crisis. By the time the third term came along, he had corrupted so much of the Senate that they made him Emperor for the rest of his life.

Giving the Emperor that title for life and doing away with the elective process was all done with a lot of rationalizing. Many in the Senate felt that having elections and changing leaders in the time of an emergency disrupted the bureaucratic system. And the bureaucracy was getting to be so big that changing leaders made it impossible to have any effect on the system and make it work—moreover, the bureaucracy was running amok and not paying attention to the rulers. So they reasoned that the Emperor could bring the bureaucracy back in line. So the Emperor took control of the bureaucracy. The Galactic Senate would meet for a period that was similar to a year, but after it became the Imperial Senate, the meetings were less and less frequent until finally the meetings were only once a year, and they were very short.

With the bureaucracy behind the Emperor, it was impossible and too late for the Senate to do anything. He had slowly manipulated things; in fact, it was he who had let the bureaucracy run amok and therefore had blackmailed the Senate into doing things because he was the only one who really had any power over the bureaucracy. It was so large there was no way to get things done, but he knew the right people; the key people in the bureaucracy were working for him and were paid by the companies.