The announcement comes the day after the loss in the Super Cup final against arch-rivals Barcelona.
According to Real Madrid, which called Alonso a club legend in the press release, the decision was made jointly.
"Real Madrid will always be his home," the club wrote.
The 44-year-old Spaniard's stay was therefore only six months long, after spending five years at the club as a player.
42-year-old Álvaro Arbeloa, also a former Real Madrid player, has been promoted from the B team and will take over as first-team coach.
Real Madrid is second in the league table, four points behind league leaders Barcelona.
