The Republican-led state Senate moved on Tuesday to install Dean G. Skelos, a Long Island senator for more than two decades, as its new majority leader. Mr. Skelos, who will replace Joseph L. Bruno, the powerful majority leader who said on Monday that he would not seek re-election, is expected to be elected by his colleagues in a closed-door conference later in the day. The selection of Mr. Skelos was confirmed by Thomas Libous, a Republican senator from Binghamton who was widely seen as the Long Island senator’s rival for the job.