Greenbrier is a city in Robertson County, Tennessee, United States. The population was 6,433 at the 2010 census, and at the 2020 census th…Greenbrier is a city in Robertson County, Tennessee, United States. The population was 6,433 at the 2010 census, and at the 2020 census the population was 6,898. According to the United States Census Bureau, the city has a total area of 6.6 square miles, of which 6.6 square miles is land and 0.04 square mile is water. The city is concentrated along a stretch of U.S. Route 41, southeast of Springfield and northwest of Goodlettsville. Greenbrier lies about 23 miles north of Nashville.