According to the Science Fiction Citations site, the earliest known use of "Terran" as a noun meaning "an inhabitant of the planet Earth" (aka Earthian, Earthie, Earthling, Earthman, Tellurian, Terrestrial, Terrestrian, etc.) was in Astounding Science-Fiction, May 1946, in part 3 of the serialization of George O. Smith's novel Pattern for Conquest:
The mission, not entirely understood by the Terrans, consists of destroying a machine sent forth by the Loard-vogh, a race that is conquering the Galaxy on a twenty-thousand-year program. This machine restricts mental activity through a vast area, thus permitting the Loard-vogh to advance without difficulty. Communication between the Little People of Tlembo and Terrans is also restricted by the machine, and so the true nature of the mission is not really known.
The earliest citation for "Terran" as an adjective is from the same 1946 George O. Smith story:
"Seventeen million of the Loard-vogh died in the Battle of Sol, and more than half of them perished because Terran spores crept into chinks in their space armor. Chinks so small that they do not permit loss of air in space.
However, the form "Terrane" was seen earlier, in the 1881 novel Three Hundred Years Hence by William Delisle Hay:
I am speaking of the Terrane Exodus and the Cities of the Sea.
The earliest citation for "Terra" as a name for the planet Earth is from an 1871 lecture "Science & Revelation" by Robert Payne Smith:
Now, let us suppose ourselves philosophers come, we will say, form the planet Jupiter, on a mission intrusted to us by the Jovians, to examine and report upon the nature of the creatures which people the four inferior planets, Terra, Venus, Mercury, and Mars.
Jeff Prucher, an associate of the Science Fiction Citations site, wrote the following essay on "Earthlings" in his Hugo-winning book Brave New Words: The Oxford Dictionary of Science Fiction:
In science fiction, when beings from different worlds encounter each other, they are generally named by their planet or star of origin; thus Martians are from Mars, and Sirians are from some hypothetical planet orbiting the star Sirius. While there are generally few terms in use for beings from any given planet or solar system, there is much greater variety in the terms for people who are from Earth. Many of these terms have been in use for centuries in other senses. Some, such as Earthling and Terrestrial, originally designated earthly (as opposed to heavenly or spiritual) beings. Terrestrian was once an adjective used to describe animals that lived on land rather than in water. Earth-man and -woman once referred only to beings that were associated with soil or the ground in some way; once SF writers got hold of them, they added Earth-folk, Earth-girl, and Earth-person as variations. SF writers also coined the fairly common terms Terran, Tellurian (after Tellus, the Roman goddess of the earth), Earther, Earthian, and Earthie, in addition to many more that never quite caught on, including Earthan, Terrene, and Terrestial. However, when faced with creatures from another star system entirely, beings from the Moon or Jupiter may seem slightly less alien, and so the word Solarian was coined to refer to any inhabitant of Earth's solar system, human or otherwise—Earthling, Martian, and Plutonian alike.