Alonso will formally take charge on July 1 as the replacement for Liam Rosenior, who was fired last month.
He will become the fifth permanent coach appointed by Chelsea's American owners Todd Boehly and Clearlake Capital since they bought the club in 2022.
Alonso lasted eight months at Madrid before leaving the club by mutual consent in January after poor results and widespread reports that he had lost control of the locker room.
That damaged his strong reputation built at Bayer Leverkusen, who he led to the German title and an unbeaten domestic campaign in the 2023-24 season.
Chelsea described Alonso as "one of the most respected figures in the modern game".
"From my conversations with the ownership group and sporting leadership, it is clear we share the same ambition," Alonso said in a Chelsea statement.
"We want to build a team capable of competing consistently at the highest level and fighting for trophies."
Chelsea look highly unlikely to be in next season's Champions League, and might miss out on European competition entirely.
The Blues were guaranteed a trophy-less season by losing to Manchester City in the FA Cup final on Saturday, though they did win the Club World Cup last year.
After an unseemly end to Rosenior's tenure, Chelsea's ownership said it would be undertaking "a process of self-reflection" ahead of its next coaching appointment, amid growing tension among supporters about the direction of an increasingly dysfunctional club and financial concerns following years of heavy spending.
Since the 2022 purchase of Chelsea by a consortium fronted by Boehly, part-owner of the Los Angeles Dodgers, and largely funded by private equity company Clearlake Capital, the club's leadership has spent about $US2.5 billion ($A3.5 billion) on new, mostly young and unproven players on long contracts.
Chelsea's most recent financial results revealed the club made pre-tax losses of $US350 million ($A490 million) - a record in the Premier League era.
It's with this backdrop that Alonso moves to Chelsea, which he described as "one of the biggest clubs in world football".
"There is great talent in the squad and huge potential at this football club and it will be my great honour to lead it," he said. "Now the focus is on hard work, building the right culture and winning trophies."
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