The first successful device I am aware of was made by Dr. Cledo Brunetti, an engineer at the US Bureau of Standards. He produced his first working model in 1947. This was pre-solid state design so it came complete with miniature vacuum tubes. But his was not an Am radio, it was meant as a real deal Dick Tracey radio designed to operate from 460-470 megacycles. it only weighted 3 ounces. It was never produced commercially. There was a toy version manufactured that was really just a tiny crystal kit that worked like crap. Still, in 1951 Hugo Gernsback predicted the manufacture of such a device "an excellent superheterodyne receiver, no larger than a wrist watch." The transistor had debuted in 1950 so the idea was no longer a lark.
In April 1952 two engineers at Western Electric come up with a wrist radio that was only 1.5" x 2" x 3.25". It was wrist watch sized, but still did not include the speaker, antenna or battery. In 1963 M.E. Quisenberry designed a one transistor wrist-radio with a single earphone. The US Signal Corps made their own version that used 3 transistors and a tiny mercury battery. It's antenna ran up your sleeve. The book The Portable Radio in American Life by Michael B. Schiffer has some great pictures of it.
Form thereon home brew wrist radios littered the classified of Popular Mechanics. Huckert Electronics sold a model by direct mail starting in 1954. In 1956 there were 2.5 ounce semi-complete wrist radios for sale in the back of magazines marketed to teens like Boys Life. It cost almost $30, was the size of a pack of cigarettes and clearly the antenna was still external but it was a bit sleeker looking. In 1964 Mellinger sold another model for $3, with a 1/8" headphone jack that really fit the basic idea. Finally in 1976 there were commercially available $10 wrist radios that was self contained loudspeaker, battery and antenna. These duly qualify but were over-sized. By the mid 1980s LCD wrist watches with AM radio were small, and readily available for a mere $15. But there was still future times to be predicted. A 1970 article in Popular science wrote:
"...by the end of this century the most common type of watch will be a form of wrist radio. It would decode and display a super-accurate time signal received from a communications satellite. Some models would include transmitters by which their wearers could keep a central office computer informed of their whereabouts."