Har Gobind Khorana was born to Indian parents Shrimati Krishna Krishna Devi Khorana and Shri Ganpat Rai Khorana in Raipur, a village in Punjab, British India at the time, which later became Pakistan. The exact date of his birth is not certain but he believed that it might have been 9 January 1922; this date was later shown in some documents, and has been widely accepted. He was the youngest of five children. His Father was a patwari, a village agricultural taxation clerk in the Indian government. In his autobiography, Khorana wrote this summary: "Although poor, my Father was dedicated to educating his children and we were practically the only literate family in the village inhabited by about 100 people." The first four years of his education were provided under a tree, a spot that was, in effect, the only school in the village.

He attended D.A.V. High School in Multan, in West Punjab, an area that is now in Pakistan. Later, he studied at the Punjab University in Lahore, with the assistance of scholarships, where he obtained a bachelor's degree in 1943 and a Master of Science degree in 1945.

Khorana lived in British India until 1945, when he moved to England to study organic chemistry at the University of Liverpool on a Government of India Fellowship. He received his PhD in 1948 advised by Roger J. S. Beer. The following year, he pursued postdoctoral studies with Professor Vladimir Prelog at ETH Zurich in Switzerland. He worked for nearly a year on alkaloid chemistry in an unpaid position.

During a brief period in 1949, he was unable to find a job in his original home area in the Punjab, which was in Pakistan by that time. He returned to England on a fellowship to work with George Wallace Kenner and Alexander R. Todd on peptides and nucleotides. He stayed in Cambridge from 1950 until 1952.

Har Gobind Khorana married Esther Elizabeth Sibler in 1952. They had met in Switzerland and had three children, Julia Elizabeth, Emily Anne, and Dave Roy.

In 1960 Khorana accepted a position as co-director of the Institute for Enzyme Research at the Institute for Enzyme Research at the University of Wisconsin at Madison. He became a professor of biochemistry in 1962 and was named Conrad A. Elvehjem Professor of Life Sciences at Wisconsin–Madison. While at Wisconsin, "he helped decipher the mechanisms by which RNA codes for the synthesis of proteins" and "began to work on synthesizing functional genes" according to the American Chemical Society. During his tenure at this University, he completed the work that led to sharing the Nobel prize. The Nobel web site states that it was "for their interpretation of the genetic code and its function in protein synthesis". Har Gobind Khorana's role is stated as follows: he "made important contributions to this field by building different RNA chains with the help of enzymes. Using these enzymes, he was able to produce proteins. The amino acid sequences of these proteins then solved the rest of the puzzle."

He became a US citizen in 1966. Beginning in 1970, Khorana was the Alfred P. Sloan Professor of Biology and Chemistry at the Massachusetts Institute of Technology and later, a member of the Board of Scientific Governors at The Scripps Research Institute. He retired from MIT in 2007.

Their Nobel lecture was delivered on 12 December 1968. Khorana was the first scientist to chemically synthesize oligonucleotides. This achievement, in the 1970s, was also the world's first synthetic gene; in later years, the process has become widespread. Subsequent Scientists referred to his research while advancing genome editing with the CRISPR/Cas9 system.

Other honours included the Louisa Gross Horwitz Prize from Columbia University and the Lasker Foundation Award for Basic Medical Research, both in 1969, the Willard Gibbs Medal of the Chicago section of the American Chemical Society, in 1974, the Gairdner Foundation Annual Award, in 1980 and the Paul Kayser International Award of Merit in Retina Research, in 1987.

After the middle of the 1970s, his lab studied the biochemistry of bacteriorhodopsin, a membrane protein that converts light Energy into chemical Energy by creating a proton gradient. Later, his lab went on to study the structurally related visual pigment known as rhodopsin.

In addition to sharing the Nobel prize (while he was working at the University of Wisconsin in the U.S.), Khorana was elected as Foreign Member of the Royal Society (ForMemRS) in 1978. The University of Wisconsin-Madison, the Government of India (DBT Department of Biotechnology), and the Indo-US Science and Technology Forum, in 2007, created the Khorana Program, jointly. The mission of the Khorana Program is to build a seamless community of Scientists, industrialists, and social entrepreneurs in the United States and India.

The program is focused on three objectives: Providing graduate and undergraduate students with a transformative research experience, engaging partners in rural development and food security, and facilitating public-private partnerships between the U.S. and India. In 2009, Khorana was hosted by the Khorana Program and honored at the 33rd Steenbock Symposium in Madison, Wisconsin.

Har Gobind Khorana died on 9 November 2011, in Concord, Massachusetts, at the age of 89. His wife, Esther, and daughter, Emily Anne, had died earlier, but Khorana was survived by his other two children. Julia later wrote about his work as a professor. "Even while doing all this research, he was always really interested in education, in students and young people."

On 9 January 2018, a Google Doodle celebrated the achievements of Har Gobind Khorana on what would have been his 96th birthday.