He was born Harold Krotoschiner in Wisbech, Cambridgeshire, England. Kroto believes that the city of Krotoszyn (spelled Krotoschin when the area belonged to Germany) in Poland was the origin of the family. Both his parents were born in Berlin, Germany and came to Britain in their 30s as refugees; Kroto's father was Jewish and so they needed to escape the Nazis. He was raised in Bolton, Lancashire, England. In 1955 the family name was shortened to Kroto.
As a child, he became fascinated by a Meccano set (called Erector in the USA), which he credits with developing skills useful in scientific research. He was raised Jewish, but the religion never seemed to fit his own beliefs, and he has become a strong atheist. He developed an interest in chemistry, physics, and mathematics in secondary school, and because his chemistry teacher in sixth form (last year of secondary school) believed that the University of Sheffield had the best chemistry department in the United Kingdom, he went to Sheffield.
In 1961 he took a B. Sc honors degree at Sheffield, followed by a Ph. D at the same institution in 1964. His doctoral research involved high-resolution electronic spectra of free radicals produced by flash photolysis (breaking of chemical bonds by light). Among other things, his doctoral studies included some research on carbon suboxide, O=C=C=C=O, and this led to a general interest in molecules containing chains of carbon atoms with numerous multiple bonds. He started his work with an interest in organic chemistry, but when he learned about spectroscopy it inclined him to quantum chemistry.
In 1963 he married Margaret Henrietta Hunter.
After some research at the National Research Council in Canada and Bell Laboratories in the United States of America he began teaching and research at the University of Sussex in England in 1967. He became a full professor in 1985, and Royal Society Research Professor in 1991.
In the 1970s he launched a research program at Sussex to look for carbon chains in interstellar space. Earlier studies had detected the molecule cyanoacetylene, H-C=C-C=N. Kroto's group searched for spectral evidence of longer similar molecules such as cyanobutadiyne, H-C=C-C=C-C=N and cyanohexatriyne, H-C=C-C=C-C=C-C=N, and found them in 1975-1978. Trying to explain them led to the formulation of the concept of the C60 molecule. (See buckminsterfullerene.) He heard of laser spectroscopy work being done by Richard Smalley and Robert Curl at Rice University in Texas, and thought he could use their apparatus to simulate the temperatures in space and create C60. The three synthesized it in 1984, leading to the Nobel Prize in Chemistry shared by the three in 1996.
He retains an interest in the chemistry of the fullerenes.