Swan was born in Glasgow, joining the merchant navy at 17, and afterwards the Royal Navy.  For a period he became a fisherman, then a mate on a commercial sailing barge. Recovering from a long illness, he took up painting and studied at schools of art at Glasgow and Arbroath.

By 1949 Donald had moved to Cornwall, where he studied pottery with Bernard LEACH and Michael LEACH, before setting up his own pottery at Castle-an-Dynas with his Cornish wife, Elizabeth. Many of his portraits feature his wife. During his sojourn in Cornwall he also assisted at the Newlyn Art Gallery, volunteering to help curate exhibitions, and he also took students of his own (one of whom was David DYER).

In 1972, he returned to Scotland, where he continued to paint portraits but also developed his maritime painting, becoming known for his historical clipper ships (incl 'Cutty Sark' which hangs on that ship) and other forms of shipping and naval pieces.

Back in Cornwall by 2001, Martin Val Baker welcomed a large solo show of the paintings of Donald Swan at the Rainyday Gallery on Market Jew Street, Penzance in February and March of 2002. 

A portrait by this artist, of the co-curator of NAG in the 1950s, the poet Wallace Nichols, is part of the Permanent Collection of NAG. His painting John in his Red Raincoat (1965) is at PENLEE HOUSE MUSEUM & ART GALLERY PENZANCE.