Michelson was born in Strzelno, Province of Posen in Germany (now Poland), the son of Samuel Michelson and his wife, Rozalia Przyłubska, both of Jewish descent. He moved to the US with his parents in 1855, at the age of two. He grew up in the mining towns of Murphy's Camp, California and Virginia City, Nevada, where his father was a merchant. His family was Jewish by birth but non-religious, and Michelson himself was a lifelong agnostic. He spent his high school years in San Francisco in the home of his aunt, Henriette Levy (née Michelson), who was the mother of author Harriet Lane Levy.

As early as 1869, while still serving as an officer in the United States Navy, Michelson started planning a repeat of the rotating-mirror method of Léon Foucault for measuring the speed of light, using improved optics and a longer baseline. He conducted some preliminary measurements using largely improvised equipment in 1878, about the same time that his work came to the attention of Simon Newcomb, Director of the Nautical Almanac Office who was already advanced in planning his own study. Michelson published his result of 299,910 ± 50 km/s in 1879 before joining Newcomb in Washington DC to assist with his measurements there. Thus began a long professional collaboration and friendship between the two.

Michelson was fascinated with the sciences, and the Problem of measuring the speed of light in particular. While at Annapolis, he conducted his first experiments of the speed of light, as part of a class demonstration in 1877. His Annapolis experiment was refined, and in 1879, he measured the speed of light in air to be 299,864 ± 51 kilometres per second, and estimated the speed of light in vacuum as 299,940 km/s, or 186,380 mi/s. After two years of studies in Europe, he resigned from the Navy in 1881. In 1883 he accepted a position as professor of physics at the Case School of Applied Science in Cleveland, Ohio and concentrated on developing an improved interferometer. In 1887 he and Edward Morley carried out the famous Michelson–Morley experiment which failed to detect evidence of the existence of the luminiferous ether. He later moved on to use astronomical interferometers in the measurement of stellar diameters and in measuring the separations of binary stars.

Simon Newcomb, with his more adequately funded project, obtained a value of 299,860 ± 30 km/s, just at the extreme edge of consistency with Michelson's. Michelson continued to "refine" his method and in 1883 published a measurement of 299,853 ± 60 km/s, rather closer to that of his mentor.

In 1887 he collaborated with colleague Edward Williams Morley of Western Reserve University, now part of Case Western Reserve University, in the Michelson–Morley experiment. Their experiment for the expected motion of the Earth relative to the aether, the hypothetical medium in which light was supposed to travel, resulted in a null result. Surprised, Michelson repeated the experiment with greater and greater precision over the next years, but continued to find no ability to measure the aether. The Michelson-Morley results were immensely influential in the physics community, leading Hendrik Lorentz to devise his now-famous Lorentz contraction equations as a means of explaining the null result.

In 1889 Michelson became a professor at Clark University at Worcester, Massachusetts and in 1892 was appointed professor and the first head of the department of physics at the newly organized University of Chicago.

In 1899, he married Edna Stanton. They raised one son and three daughters.

In 1906, a novel electrical method was used by E. B. Rosa and the National Bureau of Standards to obtain a value for the speed of light of 299,781 ± 10 km/s. Though this result has subsequently been shown to be severely biased by the poor electrical standards in use at the time, it seems to have set a fashion for rather lower measured values.

In 1907, Michelson had the honor of being the first American to receive a Nobel Prize in Physics "for his optical precision instruments and the spectroscopic and metrological investigations carried out with their aid". He also won the Copley Medal in 1907, the Henry Draper Medal in 1916 and the Gold Medal of the Royal Astronomical Society in 1923. A crater on the Moon is named after him.

The precision of their equipment allowed Michelson and Morley to be the first to get precise values for the fine structure in the atomic spectral lines for which in 1916 Arnold Sommerfeld gave a theoretical explanation, introducing the fine-structure constant.

From 1920 and into 1921 Michelson and Francis G. Pease became the first individuals to measure the diameter of a star other than the Sun. They used an astronomical interferometer at the Mount Wilson Observatory to measure the diameter of the super-giant star Betelgeuse. A periscope arrangement was used to obtain a densified pupil in the interferometer, a method later investigated in detail by Antoine Émile Henry Labeyrie for use in "Hypertelescopes". The measurement of stellar diameters and the separations of binary stars took up an increasing amount of Michelson's life after this.

In 1922, the U.S. Coast and Geodetic Survey began two years of painstaking measurement of the baseline using the recently available invar tapes. With the baseline length established in 1924, measurements were carried out over the next two years to obtain the published value of 299,796 ± 4 km/s.

Famous as the measurement is, it was beset by problems, not least of which was the haze created by the smoke from forest fires which blurred the mirror image. It is also probable that the intensively detailed work of the geodetic survey, with an estimated error of less than one part in 1 million, was compromised by a shift in the baseline arising from the Santa Barbara earthquake of June 29, 1925, which was an estimated magnitude of 6.3 on the Richter scale.

The period after 1927 marked the advent of new measurements of the speed of light using novel electro-optic devices, all substantially lower than Michelson's 1926 value.

Michelson sought another measurement, but this time in an evacuated tube to avoid difficulties in interpreting the image owing to atmospheric effects. In 1929, he began a collaboration with Francis G. Pease and Fred Pearson to perform a measurement in a 1.6 km tube 3 feet in diameter at the Irvine Ranch near Santa Ana, California. In multiple reflections the light path was increased to 5 miles. For the first time in history the speed of light was measured in an almost perfect vacuum of 0.5 mm of mercury. Michelson died with only 36 of the 233 measurement series completed and the experiment was subsequently beset by geological instability and condensation problems before the result of 299,774 ± 11 km/s, consistent with the prevailing electro-optic values, was published posthumously in 1935.

In an episode of the television series Bonanza ("Look to the Stars", broadcast March 18, 1962), Ben Cartwright (Lorne Greene) helps the 16-year-old Michelson (portrayed by 25-year-old Douglas Lambert (1936–1986)) obtain an appointment to the U.S. Naval Academy, despite the opposition of the bigoted town schoolteacher (played by william Schallert). Bonanza was set in and around Virginia City, Nevada, where Michelson lived with his parents prior to leaving for the Naval Academy. In a voice-over at the end of the episode, Greene mentions Michelson's 1907 Nobel Prize.

Norman Fitzroy Maclean wrote an essay "Billiards is a Good Game"; published in The Norman Maclean Reader (ed. O. Alan Weltzien, 2008), it is an appreciation of Michelson from Maclean's vantage point as a graduate student regularly watching him play billiards.

New Beast Theater Works in collaboration with High Concept Laboratories produced a 'semi-opera' about Michelson, his obsessive working style and its effect on his family life. The production ran from February 11 to February 26, 2011 in Chicago at The Building Stage. Michelson was portrayed by Jon Stutzman. The play was directed by David Maral with music composed by Joshua Dumas.

There has been some historical controversy over whether Albert Einstein was aware of the Michelson–Morley results when he developed his theory of special relativity, which pronounced the aether to be "superfluous." In a later interview, Einstein said of the Michelson–Morley experiment, "I was not conscious it had influenced me directly... I guess I just took it for granted that it was true." Regardless of Einstein's specific knowledge, the experiment is today considered the canonical experiment in regards to showing the lack of a detectable aether.

Numerous awards, lectures, and honors have been created in Albert A. Michelson’s name. Some of the current awards and lectures named for Michelson include the following: the Bomem-Michelson Award and Lecture annually presented until 2017 by the Coblentz Society; the Michelson-Morley Award and Lecture, along with the Michelson Lecture Series, and the Michelson Postdoctoral Prize Lectureship, all of which are given annually by Case Western Reserve University; the A.A. Michelson Award presented every year by the Computer Measurement Group; the Albert A. Michelson Award given by the Navy League of the United States; and the Michelson Memorial Lecture Series presented annually by the Division of Mathematics and Science at the U.S. Naval Academy.