In the Making of the Empire Strikes Back, I found this quote on page 224:

‘“Ben Kenobi’s outfit now seems to have turned into this costume of the Jedi Knights, really,” says Mollo. “Yoda wears a variant of the same thing.
We found this raw silk from India and it was just perfect,” says Kershner. “It hung nicely and it looked homemade. We had a piece left over, so I had a jacket made out of it for myself.”’

So John Mollo, the costume designer on Empire, seems to have been the first to have made it their costume.