David Brewster was born in Jedburgh on 11 December 1781, and was attending Edinburgh University classes at the age of twelve in 1793. It was his ambition to go into the Church. Indeed, Brewster gave his first sermon in March 1804 but nervousness led him to abandon this career. That year he became tutor to a family in Dumfriesshire and he remained there until 1807 while he pursued scientific studies and the study of literature.

In 1807, Brewster was a candidate for the Chair of Mathematics at St. Andrews University, but without success. In 1813, he submitted a paper to the Royal Society of London on Some properties of light and the same year he published a Treatise on new philosophical instruments. In 1814, illness prompted him to visit Paris and Geneva and on his return to Britain he continued publishing. In 1815, he became a Fellow of the Royal Society. In 1816, Brewster invented the kaleidoscope and although he patented the invention, it was quickly pirated because of a fault in the registration. He published his Treatise on the kaleidoscope in 1819.

Together with the mineralogist Professor Robert Jameson, he edited the Edinburgh philosophical journal, previously called the Edinburgh magazine, and in 1819 when the name changed again to the Edinburgh journal of science he was the sole editor. In 1820, Brewster became a member of the Institute of Civil Engineers in London, and in 1821 he was active in the formation of the Royal Scottish Society of Arts of which he became director. In 1822, he became a member of the Royal Irish Academy of Arts and Sciences.

In December 1837, he became the Principal of the United College of St. Salvator and St. Leonard at St. Andrews University. In 1859 he became Principal of Edinburgh University. Sir David Brewster died from an attack of pneumonia at Allerly, Melrose, on 10 February 1868.