The Galveston County City Council on Thursday approved a specific-use permit for the planned $4.5 million facility.
The Galveston Landmark Commission has asked that the design of the building, which would also house a visitor information center and bus station, be modified to look more like other 19th-century buildings on The Strand.
The Galveston County Daily News reports the center would be the first significant construction in the Strand National Historic Landmark District in decades.
Mitchell Historic Properties has a 40-year lease. The company will share with the city any profits from the center's retail rentals and parking fees.