David Brewster was born at Jedburgh, Scotland, where his father, a teacher of high reputation, was rector of the grammar school. At the age of twelve, he was sent to the University of Edinburgh, being intended for the clergy. However, he had already shown a strong inclination for natural science, and this had been fostered by his intimacy with a "self-taught philosopher, astronomer and mathematician," as Sir Walter Scott called him, of great local fame—James Veitch of Inchbonny, who was particularly skillful in making telescopes.

Though he duly finished his theological studies and being licensed to preach, Brewster's other interests distracted him from the duties of his profession. In 1799 fellow-student, Henry Brougham, persuaded him to study the diffraction of light. The results of his investigations were communicated from time to time in papers to the Philosophical Transactions of London and other scientific journals. The fact that other philosophers, notably Etienne Louis Malus and Augustin Fresnel, were pursuing the same investigations contemporaneously in France does not invalidate Brewster's claim to independent discovery, even though in one or two cases the priority must be assigned to others. A lesser-known classmate of his, Thomas Dick, also went on to become a popular astronomical writer.

The most important subjects of his inquiries can be enumerated under the following five headings:

1. The laws of light polarization by reflection and refraction, and other quantitative laws of phenomena
2. The discovery of the polarizing structure induced by heat and pressure
3. The discovery of crystals with two axes of double refraction, and many of the laws of their phenomena, including the connection between optical structure and crystalline forms
4. The laws of metallic reflection
5. Experiments on the absorption of light.

In this line of investigation, the prime importance belongs to the discovery

1. of the connection between the refractive index and the polarizing angle
2. of biaxial crystals, and
3. of the production of double refraction by irregular heating.

These discoveries were promptly recognized. As early as 1807 the degree of LL.D. was conferred upon Brewster by Marischal College, Aberdeen; in 1815 he was made a member of the Royal Society of London, and received the Copley medal; in 1818 he received the Rumford Medal of the society; and in 1816 the French Institute awarded him one-half of the prize of three thousand francs for the two most important discoveries in physical science made in Europe during the two preceding years. In 1821, he was made a foreign member of the Royal Swedish Academy of Sciences.

Among the non-scientific public his fame spread more effectually by his invention in about 1815 of the kaleidoscope, for which there was a great demand in both the United Kingdom and the United States. An instrument of greater interest, the stereoscope, which, though of much later date (1849), and along with the kaleidoscope did more than anything else to popularize his name, was not, as has often been asserted, the invention of Brewster. Sir Charles Wheatstone discovered its principle and applied it as early as 1838 to the construction of a cumbersome but effective instrument, in which the binocular pictures were made to combine by means of mirrors. Brewster's contribution was the suggestion to use prisms for uniting the dissimilar pictures; and accordingly the lenticular stereoscope may fairly be said to be his invention.

A much more valuable and practical result of Brewster's optical researches was the improvement of the British lighthouse system. Although Fresnel, who had also the satisfaction of being the first to put it into operation, perfected the dioptric apparatus independently, Brewster was active earlier in the field than Fresnel, describing the dioptric apparatus in 1812. He pressed its adoption on those in authority at least as early as 1820, two years before Fresnel suggested it and it was finally introduced into lighthouses mainly through his persistent efforts.

Brewster is noted as the inventor of the sea thermometer.

Although Brewster's own discoveries were important, they were not his only service to science. He began writing in 1799 as a regular contributor to the Edinburgh Magazine, of which he acted as editor at the age of twenty. In 1807, he undertook the editorship of the newly projected Edinburgh Encyclopaedia, of which the first part appeared in 1808, and the last not until 1830. The work was strongest in the scientific department, and many of its most valuable articles were from the pen of the editor. At a later period he was one of the leading contributors to the Encyclopædia Britannica (seventh and eighth editions) writing, among others, the articles on electricity, hydrodynamics, magnetism, microscope, optics, stereoscope, and voltaic electricity.

In 1819 Brewster undertook further editorial work by establishing, in conjunction with Robert Jameson (1774–1854), the Edinburgh Philosophical Journal, which took the place of the Edinburgh magazine. The first ten volumes (1819–1824) were published under the joint editorship of Brewster and Jameson, the remaining four volumes (1825–1826) being edited by Jameson alone. After parting company with Jameson, Brewster started the Edinburgh Journal of Science in 1824, sixteen volumes of which appeared under his editorship during the years 1824–1832, with very many articles from his own pen.

He contributed between three and four hundred papers to the transactions of various learned societies, and few of his contemporaries wrote as much for the various reviews. In the North British Review alone seventy-five articles of his appeared. A list of his larger separate works will be found below. Special mention, however, must be made of the most important of them all–his biography of Sir Isaac Newton. In 1831 he published a short popular account of the philosopher's life in Murray's Family Library; but it was not until 1855 that he was able to issue the much fuller Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton, a work which embodied the results of more than twenty years' investigation of original manuscripts and other available sources.

Brewster's position as editor brought him into frequent contact with the most eminent scientific men, and he was naturally among the first to recognize the benefit that would accrue from regular communication among those in the field of science. In a review of Charles Babbage's book Decline of Science in England in John Murray's Quarterly Review, he suggested the creation of "an association of our nobility, clergy, gentry and philosophers". This was taken up by various Declinarians and found speedy realization in the British Association for the Advancement of Science. Its first meeting was held at York in 1831; and Brewster, along with Babbage and Sir John F. W. Herschel, had the chief part in shaping its constitution.

In the same year in which the British Association held its first meeting, Brewster received the honour of knighthood and the decoration of the Guelphic order of Hanover. In 1838, he was appointed principal of the united colleges of St Salvator and St Leonard, University of St Andrews. In 1849, he acted as president of the British Association and was elected one of the eight foreign associates of the Institute of France in succession to J. J. Berzelius; and ten years later, he accepted the office of principal of the University of Edinburgh, the duties of which he discharged until within a few months of his death.

Of a high-strung and nervous temperament, Brewster was somewhat irritable in matters of controversy; but he was repeatedly subjected to serious provocation. He was a man of highly honourable and fervently religious character. In estimating his place among scientific discoverers, the chief thing to be borne in mind is that his genius was not characteristically mathematical. His method was empirical, and the laws that he established were generally the result of repeated experiment. To the ultimate explanation of the phenomena with which he dealt he contributed nothing, and it is noteworthy although he did not maintain to the end of his life the corpuscular theory he never explicitly adopted the wave theory of light. Few would dispute the verdict of James D. Forbes, an editor of the eighth edition of the Encyclopædia Britannica: "His scientific glory is different in kind from that of Young and Fresnel; but the discoverer of the law of polarization of biaxial crystals, of optical mineralogy, and of double refraction by compression, will always occupy a foremost rank in the intellectual history of the age." In addition to the various works of Brewster already mentioned, the following may be added: Notes and Introduction to Carlyle's translation of Legendre's Elements of Geometry (1824); Treatise on Optics (1831); Letters on Natural Magic, addressed to Sir Walter Scott (1832); The Martyrs of Science, or the Lives of Galileo, Tycho Brahe, and Kepler (1841); More Worlds than One (1854).

Brewster died in 1868, and was buried at Melrose Abbey. The physics building at Heriot Watt University is named in his honour.