Hopper was born Grace Brewster Murray in New York City. For her preparatory school education, she attended the Hartridge School in Plainfield, New Jersey. She applied for early admission to Vassar College at age 16, but was rejected (her test scores in Latin were too low); she was admitted the next year. She graduated Phi Beta Kappa from Vassar College with a bachelor's degree in mathematics and physics in 1928 and pursued her graduate education at Yale University, where she received a Master's degree in those subjects in 1930.

In 1930, she married Vincent Foster Hopper (1906–1976), who was then (and for many years afterward) on the faculty of NYU. In 1934, she earned a Ph.D. in mathematics from Yale under the direction of Øystein Ore. Her dissertation, entitled New Types of Irreducibility Criteria, was published that same year. Hopper began teaching mathematics at Vassar in 1931, and by 1941 she was an associate professor. She was divorced from Vincent Hopper in 1945. She kept his surname; she never remarried.

In 1943, Hopper obtained a leave of absence from Vassar and was sworn in to the United States Navy Reserve, one of many women to volunteer to serve in the WAVES. She had to get an exemption to enlist; she was 15 pounds below the Navy minimum weight of 120 pounds. She reported in December and trained at the Naval Reserve Midshipmen's School at Smith College in Northampton, Massachusetts. Hopper graduated first in her class in 1944, and was assigned to the Bureau of Ships Computation Project at Harvard University as a Lieutenant, junior grade. She served on the Mark I computer programming staff headed by Howard H. Aiken. Hopper and Aiken coauthored three papers on the Mark I,II,II also known as the Automatic Sequence Controlled Calculator. Hopper's request to transfer to the regular Navy at the end of the war was declined due to her age (38). She continued to serve in the United States Navy Reserve. Hopper remained at the Harvard Computation Lab until 1949, turning down a full professorship at Vassar in favor of working as a research fellow under a Navy contract at Harvard.

In 1949, Hopper became an employee of the Eckert-Mauchly Computer Corporation as a senior mathematician and joined the team developing the UNIVAC I. In the early 1950s the company was taken over by the Remington Rand corporation and it was while she was working for them that her original compiler work was done. The compiler was known as the A compiler and its first version was A-0. Later versions were released commercially as the ARITH-MATIC, MATH-MATIC and FLOW-MATIC compilers.

COBOL was defined by the CODASYL committee which extended Hopper's FLOW-MATIC language with some ideas from the IBM equivalent, the COMTRAN. However, it was her idea that programs could be written in a language that was close to English rather than in machine code or languages close to machine code (such as assembly language), which is how it was normally done at that time.

From 1967 to 1977, Hopper served as the director of the Navy Programming Languages Group in the Navy's Office of Information Systems Planning and was promoted to the rank of Captain in 1973. She developed validation software for the programming language COBOL and its compiler as part of a COBOL standardization program for the entire Navy.

In the 1970s, she pioneered the implementation of standards for testing computer systems and components, most significantly for early programming languages such as FORTRAN and COBOL. The Navy tests for conformance to these standards led to significant convergence among the programming language dialects of the major computer vendors. In the 1980s, these tests (and their official administration) were assumed by the National Bureau of Standards (NBS), known today as the National Institute of Standards and Technology (NIST).

Hopper retired from the Naval Reserve with the rank of Commander at the end of 1966. She was recalled to active duty in August 1967 for a six-month period that turned into an indefinite assignment. She again retired in 1971 but was asked to return to active duty again in 1972. She was promoted to Captain in 1973 by Admiral Elmo R. Zumwalt, Jr.

After Rep. Philip Crane saw her on a March 1983 segment of 60 Minutes, he championed H.J.RES. 341, a joint resolution in the House of Representatives which led to her promotion to Commodore by special Presidential appointment. In 1985, the rank of Commodore was renamed Rear Admiral, Lower Half. She retired (involuntarily) from the Navy on August 14, 1986. At a celebration held in Boston on the USS Constitution to celebrate her retirement, Hopper was awarded the Defense Distinguished Service Medal, the highest non-combat award possible by the Department of Defense. At the moment of her retirement, she was the oldest officer in the United States Navy, and aboard the oldest ship in the United States Navy.

She was then hired as a senior consultant to Digital Equipment Corporation, a position she retained until her death in 1992, aged 85.