I believe that this could well go to David Zindell for Neverness which was published in 1988 as it features many elements of transhumanism. Does anyone know any different?
1931: "The Jameson Satellite", a novelette by Neil R. Jones, first story in his Professor Jameson series; first published in Amazing Stories, July 1931, available at the Internet Archive; text available at Project Gutenberg.
Rating not even a cover mention, the first installment of Jones' most popular creation, "The Jameson Satellite", appeared in the July 1931 issue of Amazing Stories. The hero was Professor Jameson, the last Earthman, who became immortal through the science of the Zoromes. Jameson was obsessed with the idea of perfectly preserving his body after death and succeeded by having it launched into space in a small capsule. Jameson's body survived for 40,000,000 years, where it was found orbiting a dead planet Earth by a passing Zorome exploration ship. The Zoromes, or machine men as they sometimes called themselves, were cyborgs. They came from a race of biological beings who had achieved immortality by transferring their brains to machine bodies. They occasionally assisted members of other races with this transition (e.g. the Tri-Peds and the Mumes), allowing others to become Zoromes and join them on their expeditions, which sometimes lasted hundreds of years. So, much like the Borg of the Star Trek series, a Zorome crew could be made up of assimilated members of many different biological species. The Zoromes discovered that Jameson's body had been so well preserved that they were able to repair his brain, incorporate it into a Zorome machine body and restart it. The professor joined their crew and, over the course of the series, participated in many adventures, even visiting Zor, the Zorome homeworld, where he met biological Zoromes. The professor eventually rose to command his own crew of machine men on a new Zorome exploration ship. "The Jameson Satellite" proved so popular with readers that later installments in Amazing Stories got not only cover mentions but the cover artwork. The series eventually became some of the most popular and well-known of the 1930s pulps.
Depending on exactly how you choose to define transhumanism, Last and First Men: A Story of the Near and Far Future, published in 1930, tells the story of the far future of mankind. At various times throughout the story, man is radically altered though evolution, genetic engineering, and breeding. There are many times where a "current" version of man creates a new version of man.
By most definitions, this fits, and it's probably the earliest instance of genetic engineering in a novel. It does not use the term "transhumanism", though.
From another recent question on this site, Mimsy Were the Borogoves.
Published in 1943.
The philosophy of transhumanism can be traced back as far as the Epic of Gilgamesh with it's quest for immortality as a plot point ties in with the tranhumanist thought.
But it was the phisopher FM-2030 (born F.M. Esfandiary) who started using the term transhuman to identify people who adopt technologies, lifestyles and world views transitional to "posthumanity" around 1973.
Transhumanism in fiction could also be called postcyberpunk (aka cyberprep) as most transhumanist works hake place in a utopian society rather than an dystopian society akin to cyberpunk.
Bruce Bethke first coined the term cyberpunk in his series of short stories in 1983 called "Cyberpunk".
In The City and the Stars (1956), Arthur C. Clarke describes people whose bodies are created by a computer and whose memories are stored in the computer's memory banks. The design of the body has changed too:
The human body ... had changed, however, a good deal from its original primitive form, though most of the alterations were internal and not visible to the eye. Man had rebuilt himself many times in his long history, in the effort to abolish those ills to which the flesh was once heir.
Also, what about Huxley's Brave New World (1931)? I haven't read it, but it sounds like technology is being used to improve and change life.
If by transhumanism, take into account "Practical methods and visions of transforming ourselves, achieving longevity or immortality, conquering death and disease, amplifying our intelligence and minds and extending our bodies." In which case, the earliest novel to depict a descendant of human beings whose body has been radically transformed by technology is E. V. Odle's The Clockwork Man (1923).
The eponymous clockwork man is a man "a man into whose body a clock-like monitor-cum-Time Machine has been inserted – comes accidentally back through time from 8000 CE to the present". He is effectively an advanced type of cyborg and comes from world radically transformed by technology. He is able to move back and forth in time and to transform his body in numerous and quite extraordinary ways: growing bigger or smaller, working faster or slower, and even reversing or accelerating his age. In the world of the clockwork man any resource or artifact can be immediately available; it is as though everything in their world is present all at once. This is irrespective of time or space.
Finally the clockwork man's machine body resets itself and he is able to return to his own time and world.
Odle's scientific romance has been unjustifiably neglected. It contains much satire about society in 1923, and, in particular, the role of women as, yes, the book is a feminist text (despite being written by a man). The clockwork man represents a warning against certain social and cultural trends, particularly, male aggression and misogyny. There are hints that men like the clockwork men had been transformed into living machines and given access to everything they might want as a way of getting them out of the way of women and what is vaguely and elliptically hinted as a better class of men who are not in thrall to stereotypical male aggression and who prefer a more humane way of living.
While it is not well known, this scientific romance has been recently reprinted. Copies are likely to be available from your favourite online or shopfront bookshop.
The clockwork man has all the characteristics of a transhuman being. His body, like his fellows who are mentioned but not shown, has been transformed by technology. He is capable of performing prodigious feats of speed, strength and mobility, effectively shape-shift, monitor and modulate his own bodily functions at will, and travel in time and space.
In conclusion, E.V. Odle's The Clockwork Man (1923) is the earliest example of a novel about a transhuman.
Julian Huxley wrote about Transhumanism (in New Bottles for New Wine, London: Chatto & Windus, pp. 13-17) in 1957, so it was certainly in the air by then.
If you're not looking for strictly for technological enhancements or when the phrase was first coined then the earliest examples I can think of of humans taking it upon themselves to improve themselves are:
The changes to the human condition in Second Foundation are more subtle than The Naked Sun, but both show people taking it upon themselves to modify/improve human thought and physiology.