The earliest building known on this site was constructed around 1598 as the residence of the Royal Governor of East Florida, appointed by the King and Queen of Spain. It also served as the administrative headquarters of governmental functions of the city. This structure was reconstructed, renovated, and added onto several times, due to natural disasters and foreign raids. The building served as an American federal building after Florida became a United States territory in 1821, and later became the U.S. Post Office for the city of St. Augustine. The building as it appears today was constructed in 1937, designed to resemble the Governor’s Mansion of St. Augustine in the 1760s. The building became state property in 1967 and served as the headquarters of the Historic St. Augustine Preservation Board until 1997. Today it houses the Governor's House Cultural Center and Museum and Governor's House Library.
The full Wikipedia entry for Government House is available here.
A historic structures report for Government House was completed on May 2012.
Government House is located within the Plaza, thus it does not have a traditional block and lot number assigned. The standardized location for Government House is WPL, or West Plaza Lot.