Did Joseph Stalin reign as leader of the USSR from 1922 to 1953?

That is somewhat correct.

For the begginning of that time he shared the power with others. He had to slowly push them out of the picture. He gained considerable more power in 1924 at the death of Vladimir Lenin. By 1929, he successfully pushed the other political leaders of the USSR out of power, one of which included Leon Trotsky.

From 1929 to 1953 he had full and sole power of the USSR.