Calero had been on trial at the Championship outfit, and after he impressed on his short stay in the East Midlands, head coach Steve McClaren is delighted that the Spain youth international has decided to make the switch to the Rams.
The 53-year-old told the club's official website: "He's a young player with excellent pedigree. We are really pleased that he sees his future at Derby County.
"We are looking forward to working with him in order to help him develop at what is an important stage of his career."
The 19-year-old had been a regular in Atletico Madrid's 'B' team while he has also featured in the senior squad during his time at Vicente Calderon.