The peak is situated in Wrangell-St. Elias National Park and Preserve at the head of Dan Creek, 18 mi (29 km) east-southeast of McCarthy, and 4 mi (6 km) east-northeast of Williams Peak.

The peak is named after Joshua Green (1869-1975), a Seattle businessman who through his financial backing of mining ventures was instrumental in mineral development in the Dan Creek area.

Based on the Köppen climate classification, Joshua Green Peak is located in a subarctic climate zone with long, cold, snowy winters, and cool summers.

[3] Winds coming off the Gulf of Alaska are forced upwards by the Saint Elias Mountains (orographic lift), causing heavy precipitation in the form of rainfall and snowfall.

The months May through June offer the most favorable weather for viewing and climbing.