The headwaters of the Sunwapta River are near the Columbia Icefield in the valley west northwest of Sunwapta pass, which divides Jasper National Park from Banff National Park. Several kilometres down the valley from the pass is Sunwapta Lake, at the toe of the Athabasca Glacier, which is considered the nominal source for the river. The Sunwapta river then continues to run northwest through Jasper National Park, following the Icefields Parkway, and finally joins the Athabasca River shortly after Sunwapta Falls.
Sunwapta is a Stoney Indian word meaning "turbulent river." Geologist A. P. Coleman named the river in 1892.