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 US 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.
Real were knocked out of the Champions League as holders in the quarterfinals by Arsenal.
Alonso's first test will be the Club World Cup where they are in a group with Saudi side Al-Hilal, Mexican club Pachuca and Austria's RB Salzburg in the new 32-team tournament that kicks off on June 14.