Wolcott began to assume a more prominent role in Republican circles after his father's death. He was a founding member and the first president of the Young Republican Club, an organization designed to inject new life into the party. This organization promoted him as a potential candidate for lieutenant governor. In the 1892 state convention, Wolcott won the nomination despite opposition from some party leaders. Even though the Republican gubernatorial candidate, William H. Haile, lost to incumbent Democrat William Russell, Wolcott won his race. He served as the 36th Lieutenant Governor from 1893–1897, first under Russell, and then under Republican Frederic T. Greenhalge. He assumed the gubernatorial duties as Acting Governor in March 1896 as a result of the death of Greenhalge, and was later elected as the 39th Governor in November, serving from 1897 until 1900. He was reelected each year by large popular majorities.