Amat, 20, is expected to move to the suburban Madrid club in a bid to get more first-team football.
“I know I must work harder than anyone, as have the other players who have gone out on loan but returned here afterwards,” the centre-half said.
“It is my goal to return to Espanyol as it is my home, but I have to play more minutes and gain experience.
“I need to play as well as I possibly can and I am eager to take this opportunity to grow as a player. I think I can do this.”
In three years as a professional, Amat has played 71 times for the Espanyol first team, appearing for Spain at every age-group level up to U21.