The Governor of South Dakota is the chief executive of the U.S. state of South Dakota. The current Governor is Dennis Daugaard. The Governor has the power to sign or veto laws, and to call the Legislative Assembly into emergency session. He has an ex officio North Dakota Governor's Residence. The governor may only serve two terms consecutively, and becomes eligible for reelection after four years out of office. The following is a list of Governors of the state of South Dakota, United States. 1 Governors of Dakota Territory.