Nacho has won 26 trophies with Madrid, a record he shares with Luka Modric.
"Real Madrid would like to thank and express our appreciation to Nacho, one of the club's biggest legends," the club said.
The 34-year-old Nacho, who is playing with Spain at the European Championship, has been with Madrid for more than two decades, since joining the club's youth academy in 2001.
"I arrived as a 10-year-old and I've grown as a person and as a player," Nacho said in a letter to fans on social media. "For almost 25 years I've been coming every day to practice in the same place, learning the values of Madrid and giving my life and fighting for this shield. I've given everything I had."
Nacho did not say where he will play next, but Spanish media said he is set to join a team in Saudi Arabia.
Nacho played 12 seasons with Madrid after making his first-team debut in 2012, playing in 364 games and winning four Spanish leagues.
"Since he arrived at our youth academy as a child, Nacho has been an example to everyone and has earned the affection, recognition and admiration of everyone at Real Madrid," club president Florentino Pérez said. "Real Madrid is and always will be his home."