The 48-year-old has been in charge for five seasons, overseeing promotion from the third tier of Spanish football to La Liga, where they have remained for two campaigns.
Leganes are safe from relegation in 17th place and despite their league position will remember this as a fine season after they knocked Real Madrid out of the King's Cup at the quarter-final stage.
"What stands out is his commitment, his honesty, his capacity to integrate with the club's values and those of the fans, and indeed those of the whole city," Leganes said in a statement.
"Named as adopted son of the city by Leganes Council, Asier Garitano leaves an indelible memory in the minds of all his colleagues, players, the technical team, the staff and the board, and especially the fans, whom he has made very happy."
(Reporting by Rik Sharma, editing by Ed Osmond)
