I was watching a documentary on meth addiction, and it made me think of the Lotus Eaters in the Odyssey. That concept of addiction seems similar to how we think of it today, but it's the only one I've heard of until pretty recently in history.
(I know that hallucinogens were used in a religious context in many ancient cultures, but I'm referring specifically to addiction with this question.)
One eyewitness account which some consider 'solid' is the Roman physician Galen's writings regarding the opium-based drug he gave the emperor Marcus Aurelius. I'll copy and paste an earlier answer I gave here.
A very influential paper is Thomas Africa's The Opium Addiction of Marcus Aurelius. The idea is that Marcus was addicted to the opium in the drug or antidote theriac which was administered by the physician Galen. Apparently the emperor used it both as a painkiller and a sleep aid.
Galen writes that Marcus stopped taking it because it made him drowsy but then realised he couldn't sleep without it. At one point Galen says that Marcus took it daily. Galen never, to my knowledge, shows any worry about Marcus taking too much of it or that he has become hooked on it.
Marcus' biographer Anthony Birley stresses that the regular use may (emphasis his) mean Marcus was an addict, but that he did not become a helpless addict. He says: 'the attempt to discover traces of the opium eater's confused and distorted imagination in the Meditations has not been very convincing.'
Africa's article is quite dated, being published in 1961, and it does show its age in some places. Even in the very first paragraph there are several statements which I would argue against. It has become a popular belief among the public that Marcus was an addict, but I think most academics are somewhat skeptical.
So it is conceivable that there were addicts, but this is not universally accepted. And if there were addicts, as far as I know physicians didn't recognise them as such.