"I've been dreaming of this moment since the day I left, I'm very excited," Joselu told a press conference in the Spanish capital.
The forward has scored three goals in four appearances for his country and arrives from Espanyol on a year-long loan with option to buy to help Madrid reinforce a depleted attack.
Karim Benzema, Eden Hazard, Marco Asensio and Mariano Diaz have left, leaving room for major reinforcements.
"We all know Karim's level at this club, but I'm here to do a different job," he said.
"I'm going to give my all for this club, it's the club of my life, when you step onto the pitch, especially at the Bernabeu, you want to score goals."
Joselu is the club's fourth signing after midfielder Jude Bellingham, defender Fran Garcia and the return of Brahim Diaz.
The journeyman striker, who has played for 10 clubs in Spain, Germany and England, previously played for the Real Madrid B team and has one La Liga appearance for Los Blancos, in the 2010-11 season, without managing to break into the first team.
This season Joselu finished as La Liga's third top goalscorer with 16 goals despite Espanyol's relegation, earning him a call up to the national team squad for the Nations League final four.
The targetman scored a last-minute winner in the semi-final against Italy and appeared from the bench again in the final against Croatia on Sunday as Spain triumphed in the Netherlands.
