The Argentina international was cut loose by Valencia last summer as he recovered from a knee injury.
Garay said, “Many will wonder why I did not sign for any team in June, being free and being almost recovered. There is the reason, ALMOST.
"My decision was to recover 100% so that I can give everything of myself once incorporated into my next job.
"To do this, I had to make a decision, divide the final stretch of the recovery into two parts: The first in Madrid with a great team already known in my past and with excellent results. And the second, to go to another city where I considered the best professionals to be, which I have been with for the last few years at my last club.
“Now that both stages are finished, I will finish with the third one, joining what has been, is and will be my passion, football. But with a difference, 100% recovered and ready to step on the field and give everything as I have done up to now."