Green River is located at 38°59'41" North, 110°9'38" West (38.995000, -110.160833).
According to the United States Census Bureau, the city has a total area of 12.64 mi2 (32.74 km2). 12.51 mi2 (32.41 km2) of it is land and 0.13 mi2 (0.33 km2) of it is covered by water. The total area is 1.00% water.
Green River is located in the Mountain Standard Time (MST) timezone, GMT-07:00. It observes Daylight Saving Time (DST).