The river, and several other features in the area, are named after the trumpeter swans found in the region.

It arises in the northwest corner of the basin in the Porcupine Hills and flows generally south, contained in a large valley two miles (3 km) wide and 400 feet (120 m) deep, until it nears Pelly, Saskatchewan.

Here it turns northeast, collecting tributary streams off the north escarpment of the Duck Mountains, and terminates at Swan Lake.

[1] Slopes on the south escarpment of the Porcupine Hills average 100 feet per mile (19 m/km).

Communities located on its tributaries include Norquay (on Spruce Creek), and Minitonas (on the East Favel River).