The kind of being you are describing is known, aptly, as a 'Grey' (authors usually seem to opt for the UK spelling).
In addition to the physical features you describe, they are also frequently portrayed as being bald, shorter and much thinner than a human adult, and often with a tiny slit for a mouth, or no mouth at all. In the Chambers Dictionary of the Unexplained (2007, ed. Una McGovern), a Nebraska woman known as 'Jenny', under hypnosis, describes the Greys as follows:
Tinier than four feet, but bigger than three. I don't think he has hair. The head is shaped like an egg. The face is waxy - real pale, pinkish, greyish... The nose is just a tiny bump. The mouth is a slit. The eyes are long slits with nobody home.
But we are perhaps more interested not in their reality and physicality, but in the Greys as a cultural phenomenon. Ronald D. Story, editor of the excellent Encyclopedia of Extraterrestrial Encounters (2001), suggests they represent a reflection of humanity today, and a foreshadowing of our potential 'future state'. In his footnote to the entry on Greys, he describes them as follows:
Greys are sometimes good and sometimes evil, but generally they are amoral. In other words, they represent multiple aspects of the human personality - especially the contemporary human (or humanoid) - for good or ill. [...] The grey colour symbolises neutrality in morals, sexuality and emotions. It also symbolises 'grey matter', or intelligence. The eyes are large and black (wtihout pupils), like a shark's eyes [...] The hairlessness of Greys is derived from the assumption that we are losing our animal characteristics [...] They represent human evolution and its uncertain future. They are analogous of ourselves.
It's important to remember that, for much of the 20th century, the form an alien took was not as culturally fixed as it seems to be today. Greys were for a long time only one type among many. In the 1950s they made up only three per cent of reported encounters. The Field Guide to Extraterrestrials (Patrick Huyghe, 1996) is based on aliens seen between the 1940s and 1990s, and describes 50 types of creatures in four categories: Humanoid, Animalian, Robotic and Exotic. These include forms such as 'walking tombstones', gelatinous blobs, blonde-haired 'nordics', humanoid lizards and giant insects.
Bearing in mind the fact that, until perhaps the late 1980s, they weren't afforded much of a special cultural status, I have not come across any attempt at a history of Greys that predates the 1990s. Martin Kottmeyer has written detailed essays on, I suppose, the cultural 'prehistory' of the Grey. These appear in Magonia magazine, and as the entry mentioned above in the Encyclopedia of Extraterrestrial Encounters - the two are almost identical so I will draw on the latter.
Kottmeyer suggests that depictions of similar beings have appeared in art throughout history. These include in Greco-Egyptian murals, and even as 'watchmen' (angels) in the Book of Enoch, though I must admit my attempt to find this reference in the Book of Enoch was fruitless. He also cites examples of similar-looking creatures in art from Denmark and the Congo. However, he admits this is probably coincidence/artistic license.
Instead, he says, the history of the Greys begins in the 19th century, with the increasing acceptance of the theory of evolution. Ideas came forward - that the next step in evolution might see man develop an even larger brain, while progress in science and society would reduce man's reliance on having physical strength and agility. Out of these kinds of ideas, H. G. Wells devised the creatures - Morlocks and Eloi - that represented two future in The Time Machine, the latter of which Kottmeyer puts forward as a direct antecedent of the Greys, albeit a 'halfway point':
Coming through the bushes by the White Sphinx were the heads and shoulders of men running. One of these emerged in a pathway leading straight to the little lawn upon which I stood with my machine. He was a slight creature--perhaps four feet high--clad in a purple tunic, girdled at the waist with a leather belt. Sandals or buskins--I could not clearly distinguish which--were on his feet; his legs were bare to the knees, and his head was bare. ... He struck me as being a very beautiful and graceful creature, but indescribably frail. His flushed face reminded me of the more beautiful kind of consumptive--that hectic beauty of which we used to hear so much.
There is a clear cultural thread, though, that has seen the Greys invade Western and (to a lesser extent) world culture, arguably starting with the Betty and Barney Hill incident in 1961. A couple driving on U.S. Route 3 saw a strange object in the sky, stopped to take a better look, and were shocked to see small creatures working inside. Under hypnosis two years later, they recalled encountering - and being abducted by - the creatures, who were 'classic' greys, albeit clothed in contemporary fashionwear. It is notable that this was the first abduction experience to gain widespread media coverage.
Spielberg's Close Encounters of the Third Kind (1977) appears to have taken cues from the Hills' experience, depicting the aliens in a similar form and number. Ten years later, Whitley Strieber's story of alien abduction, the international bestseller "Communion", prominently featured a classic 'grey' on the cover. Underground artist Bill Barker's 'Schwa' alien head symbol became popular for a period in the early 1990s, and Greys appeared in shows like the X-Files in the mid-to-late 1990s, serving to cement them further as the depiction of extraterrestrial beings.
As a footnote, the reason I'm hesitant to say Greys have taken over the world beyond the West is that more exotic types of alien - such as little crab-walking gnomes - are still seen in places like South America.
