Olive Branch is a city in DeSoto County, Mississippi. The population was 33,484 at the 2010 census. Olive Branch is a suburb of Memphis, Tennessee and is part of the Memphis Metropolitan Statistical Area, a region that consists of three counties in southwest Tennessee, five counties in northwest Mississippi, and two counties in eastern Arkansas. From 1990 to 2010 Olive Branch was the fastest growing city in the United States with a growth rate of 838%.