In 1786 Menzies was appointed surgeon on board the Prince of Wales (Captain James Colnett), on a fur-trading voyage round Cape Horn to the northern Pacific. This ship, in company of Princess Royal (Captain Duncan), visited North America, China and Hawai'i (the Sandwich Isles) several times; Menzies collected a number of new plants on this voyage, and also ensured that none of the crew died of illness. Menzies returned to England in 1789. He was elected a fellow of the Linnean Society in 1790.
In 1790, Menzies was appointed as naturalist to accompany Captain George Vancouver on his voyage around the world on HMS Discovery. (see Vancouver Expedition) When the surgeon fell ill, Menzies took over his duties.
In 1794, while Discovery wintered in Hawai'i, Menzies, with Lieutenant Joseph Baker and two other men, made the first recorded ascent of Mauna Loa. Menzies used a portable barometer to measure the height of the mountain as 13564 feet (4134m) compared to its actual height of 13679 feet (4169m).
After the voyage, Menzies served with the Navy in the West Indies. He received the degree of M.D. at the University of Aberdeen in 1799. After retiring from the Navy he became a doctor and surgeon at Notting Hill, London. He became the leader of the Linnean Society upon the death of A.B. Lambert.
Menzies's wife died in 1837. They had no children.
Menzies himself died in London on 15 February 1842 and is buried in Kensal Green cemetery.
Menzies' name is commemorated in the scientific names of several of the plants he discovered, including Menziesia, a genus of shrubs in the Ericaceae, and the Douglas-fir Pseudotsuga menziesii, the most important tree in western North America. The Pacific madrone, an evergreen tree and largest of the Ericaceae, was named Arbutus menziesii in his honour by Friedrich Pursh. Also named for Menzies, in a corrupted form as adapted by the Nuxalk people of the Bella Coola area of the Central Coast of British Columbia, is "Bensins Island", as recorded by Alexander Mackenzie during his visit there shortly after Vancouver's ship visited the area.