This is a list of mentions I found with my short googling:
The yoga exercise technics were well-known in Asia as a both physical and mental health cure for a long time.
According to Wikipedia, Cicero said:
It is exercise alone that supports the spirits, and keeps the mind in vigor
I know about youth movements such as Sokol in the second half of the 19. century. Namely Sokol originated in the Bohemia under the inspiration of the antic athlets and the club was combining the psychological and the physical advantages of exercise.
Eastern psycho-somatic thoughts got to the Western world at the end of the 19th century with the rise of esoterism etc.
But when did physical exercise such as regular stretching technics actually get into the Western world - when it became to be "normal" to stretch?
(I don't ask about the exercise in sense of physical training - that seems to be rooted much deeper in our culture like in the training for hunt, I ask about stretching we do before physically exhausting sport today and I wonder especially, wheter it's rooted rather in science than in culture or philosophy)