Kroto was born in Wisbech, Cambridgeshire, England, to Edith and Heinz Krotoschiner, with his name being of Silesian origin. His father's family came from Bojanowo, Poland, and his mother's from Berlin. Both of his parents were born in Berlin and fled to Great Britain in the 1930s as refugees from Nazi Germany; his Father was Jewish. Harry was raised in Bolton while the British authorities interned his Father on the Isle of Man as an enemy alien during World War II and attended Bolton School, where he was a contemporary of the actor Ian McKellen. In 1955, Harold's Father shortened the family name to Kroto.

Kroto was educated at Bolton School and went to the University of Sheffield in 1958, where he obtained a first-class honours BSc degree in Chemistry (1961) and a PhD in Molecular Spectroscopy (1964). During his time at Sheffield he also was the art Editor of "Arrows" – the University student magazine, played tennis for the University team (reaching the UAU finals twice) and was President of the Student Athletics Council (1963–64). Among other things such as making the first phosphaalkenes (compounds with carbon phosphorus double bonds), his doctoral studies included unpublished research on carbon suboxide, O=C=C=C=O, and this led to a general interest in molecules containing chains of carbon atoms with numerous multiple bonds.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 towards quantum chemistry; he later developed an interest in astrochemistry.

In 1963, he married Margaret Henrietta Hunter, also a student of the University of Sheffield at the time. The couple had two sons: Stephen and David. Throughout his entire life, Kroto was a lover of film, theatre, art, and music and published his own artwork.

After obtaining his PhD, Kroto spent two-years in a postdoctoral position at the National Research Council in Ottawa, Canada carrying out further work in molecular spectroscopy, and also spent the subsequent year at Bell Laboratories in New Jersey (1966–1967) carrying out Raman studies of liquid phase interactions and worked on quantum chemistry.

In 1967, Kroto began teaching and research at the University of Sussex in England. During his time at Sussex from 1967 to 1985, he carried out research mainly focused on the spectroscopic studies of new and novel unstable and semi-stable species. This work resulted in the birth of the various fields of new chemistry involving carbon multiply bonded to second and third row elements e.g. S, Se and P. A particularly important breakthrough (with Sussex colleague John Nixon) was the creation of several new phosphorus species detected by microwave spectroscopy. This work resulted in the birth of the field(s) of phosphaalkene and phosphaalkyne chemistry. These species contain carbon double and triple bonded to phosphorus (C=P and C≡P).

In 1975, he became a full professor of Chemistry. This coincided with laboratory microwave measurements with Sussex colleague David Walton on long linear carbon chain molecules, leading to radio astronomy observations with Canadian astronomers revealing the surprising fact that these unusual carbonaceous species existed in relatively large abundances in interstellar space as well as the outer atmospheres of certain stars – the carbon-rich red giants.

This research is significant for the discovery of a new allotrope of carbon known as a fullerene. Other allotropes of carbon include graphite, Diamond and graphene. Harry Kroto's 1985 paper entitled "C60: Buckminsterfullerine", published with colleagues J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, was honored by a Citation for Chemical Breakthrough Award from the Division of History of Chemistry of the American Chemical Society, presented to Rice University in 2015. The discovery of fullerenes was recognized in 2010 by the designation of a National Historic Chemical Landmark by the American Chemical Society at the Richard E. Smalley Institute for Nanoscale Science and Technology at Rice University in Houston, Texas.

In 1995, he jointly set up the Vega Science Trust, a UK educational charity that created high quality science films including lectures and interviews with Nobel Laureates, discussion programmes, careers and teaching resources for TV and Internet Broadcast. Vega produced over 280 programmes, that streamed for free from the Vega website which acted as a TV science channel. The trust closed in 2012.

Kroto was made a Knight Bachelor in the 1996 New Year Honours list.

From 2002–2004, Kroto served as President of the Royal Society of Chemistry. In 2004, he was appointed to the Francis Eppes Professorship in the chemistry department at Florida State University, carrying out research in nanoscience and nanotechnology.

In 2003, prior to the Blair/Bush invasion of Iraq on the pretext that Iraq had weapons of mass destruction, Kroto initiated and organised the publication of a letter to be signed by a dozen UK Nobel Laureates and published in the Times. It was composed by his friend the Nobel Peace Prize Laureate the late Sir Joseph Rotblat and published in The Times on 15 February 2003.

In 2004, Kroto left the University of Sussex to take up a new position as Francis Eppes Professor of Chemistry at Florida State University. At FSU he carried out fundamental research on: Carbon vapour with Professor Alan Marshall; Open framework condensed phase systems with strategically important electrical and magnetic behaviour with Professors Naresh Dalal (FSU) and Tony Cheetham (Cambridge); and the mechanism of formation and properties of nano-structured systems. In addition, he participated in research initiatives at FSU that probed the astrochemistry of fullerenes, metallofullerenes, and polycyclic aromatic hydrocarbons in stellar/circumstellar space, as well as their relevance to stardust.

In 2008, Kroto was critical of Michael Reiss for directing the teaching of creationism alongside evolution.

In 2009, Kroto spearheaded the development of a second science education initiative, Geoset. Short for the Global Educational Outreach for Science, Engineering and Technology, GEOSET is an ever-growing online cache of recorded teaching modules that are freely downloadable to educators and the public. The program aims to increase knowledge of the sciences by creating a global repository of educational videos and presentations from leading universities and institutions.

Kroto was a "devout atheist" who thought that beliefs in immortality derive from lack of the courage to accept human mortality. He was a patron of the British Humanist Association. He was a supporter of Amnesty International. He referred to his view that religious dogma causes people to accept unethical or inhumane actions: "The only mistake Bernie Madoff made was to promise returns in this life." He held that Scientists had a responsibility to work for the benefit of the entire species. On 15 September 2010, Kroto, along with 54 other public figures, signed an open letter published in The Guardian, stating their opposition to Pope Benedict XVI's state visit to the UK.

Kroto spoke at CSICon 2011, a convention "dedicated to scientific inquiry and critical thinking" organized by the Committee for Skeptical Inquiry in association with Skeptical Inquirer magazine and the Center for Inquiry. He also delivered the IPhO 2012 lecture at the International Physics Olympiad held in Estonia.

The discovery of buckminsterfullerene caused Kroto to postpone his dream of setting up an art and graphic design studio – he had been doing graphics semi-professionally for years. However, Kroto's graphic design work resulted in numerous posters, letterheads, logos, book/journal covers, medal design, etc. He produced artwork after receiving graphic awards in the Sunday Times Book Jacket Design competition (1964) and the Moet Hennesy/Louis Vuitton Science pour l'Art Prize (1994). Other notable graphical works include the design of the Nobel UK Stamp for Chemistry (2001) and features at the Royal Academy (London) Summer Exhibition (2004).

In 2014, Kroto spoke at the Starmus Festival in the Canary Islands, delivering a lecture about his life in science, chemistry, and design.

In 2015, Kroto signed the Mainau Declaration 2015 on Climate Change on the final day of the 65th Lindau Nobel Laureate Meeting. The declaration was signed by a total of 76 Nobel Laureates and handed to then-President of the French Republic, François Hollande, as part of the successful COP21 climate summit in Paris.

Kroto died on 30 April 2016 in Lewes, East Sussex from complications of amyotrophic lateral sclerosis at the age of 76. He was surrounded by family and close friends.

Richard Dawkins wrote a memorial for Chemist Kroto where he mentioned Kroto's "passionate hatred of religion." The Wall Street Journal described him as "(spending much of his later life) jetting around the world to extol scientific education in a world he saw as blinded by religion." Slate's Zack Kopplin related a story about how Kroto gave him advice and support to fight Louisiana’s creationism law, a law that allows public school science teachers to attack evolution and how Kroto defended the scientific findings of global warming. In an obituary published in the journal Nature, Robert Curl and James R. Heath described Kroto as having an: