Dewar, the son of a wine merchant, was born at Kincardine-on-Forth in Scotland. He was educated at Edinburgh University where he was a pupil of Lyon Playfair. In 1869 he was appointed lecturer in chemistry at the Royal Veterinary College, Edinburgh, and from 1873 also held the post of assistant chemist to the Highland and Agricultural Society of Scotland. In 1875 Dewar became Jacksonian Professor of Experimental Philosophy at Cambridge University and from 1877 he was also Fullerian Professor of Chemistry at the Royal Institution, London. He did most of his work in London where the facilities for experimental work were much better.

Dewar conducted his most important work in the field of low temperatures and the liquefaction of gases. In 1878 he demonstrated Louis Cailletet's apparatus for the liquefaction of oxygen and by 1891 he was able to produce liquid oxygen in quantity. In about 1872 he devised a double-walled flask with a vacuum between its highly reflective walls, the Dewar flask, and used this to store liquefied oxygen at extremely low temperatures. This vessel (the thermos flask) has come into everyday use for keeping substances either hot or cold.

Hydrogen had so far resisted liquefaction and Dewar now turned his attention to this. Using the Joule–Thomson effect together with Karl von Linde's improvements of this, he produced a machine with which he obtained temperatures as low as 14 K and he produced liquid hydrogen in 1898 and solid hydrogen in 1899. Only helium now resisted liquefaction; this was achieved by Heike Kamerlingh-Onnes in 1908.

From about 1891 Dewar also studied explosives and with Frederick Abel he developed the smokeless powder, cordite. He was knighted in 1904.