The 24-year-old, who has played for Greece at junior level, began his career at Greek side Ergotelis before moving to Olympiacos in 2013.
Bouchalakis went on to win three Greek Super League titles during his four years with the national giants and also featured in the Europa League and Champions League.
"We have taken the decision to sign him. We are delighted with his contribution. He has done very well," Forest manager Mark Warburton told the Nottingham Post.
"I said before that I was not sure about him at first. But he has impressed us since, after the first few days in Florida. He has impressed in training and he impressed against Notts County. He was impressive again when he came on against Mansfield.
"I have been happy with his contribution and I am glad to welcome him on board. I am looking forward to having him as a Nottingham Forest player."