The mountain was named by Arthur Oliver Wheeler for Rev.

William Spotswood Green (1847–1919), who explored, mapped, named, climbed, and wrote about the Selkirk Mountains.

He is credited with recommending the location for a small chalet to the Canadian Pacific Railway that would grow to become the Chateau Lake Louise hotel, as well as making the first ascent of Mount Bonney.

[1] Based on the Köppen climate classification, Mount Green is located in a subarctic climate zone with cold, snowy winters, and mild summers.

Precipitation runoff from the mountain drains north into the Illecillewaet River.