Alonso has signed a three-year contract until June 2028, the club said in a statement. The 43-year-old replaces Carlo Ancelotti, who took charge of his last game on Saturday.
With Ancelotti finishing his second stint at Real without winning a major trophy, Real moved quickly to change coaches after the Italian veteran agreed to coach Brazil
Alonso had been in charge of Bayer Leverkusen and confirmed he would be leaving the German club this month.
The Spaniard took charge of Leverkusen in October 2022 and guided them to the double last season as they lifted their first Bundesliga title without losing a game. They also won the German Cup and reached the Europa League final.
He had a contract at Leverkusen until 2026 but the club said they had granted his wish to terminate his deal at the end of the season.
Alonso will be presented as Real coach on Monday and will take charge from June 1, ahead of the Club World Cup which starts in the United States next month.
The former Spain international joined Real in 2009 from Liverpool and made 236 appearances for them, winning a LaLiga title, two Copa del Rey trophies and the club's long-awaited 10th European crown.
He began his coaching career at Real's youth academy where he managed the Under-14 team during the 2018-19 season, winning the league and the Champions tournament.
He took charge of Real Sociedad's reserve team before making the big step up to take the Leverkusen job.
Alonso will hope to follow in the footsteps of another Real Madrid midfielder, Zinedine Zidane, who returned to coach the Spanish club and won three Champions League titles in a row.
Under Ancelotti, Real will finish second in LaLiga behind Barcelona, who also beat them in the Spanish Super Cup and Copa del Rey finals this season.
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