The announcement comes just a day after Chelsea, under interim coach Calum McFarlane, lost the FA Cup final to Manchester City 0-1.
The former midfielder has agreed to manage Chelsea for the next four years.
"Chelsea is one of the biggest clubs in world football and it is a huge honour to become the manager of this fantastic club," he said in a statement on the club's website.
The last permanent head coach at Chelsea was Liam Rosenior, who was fired earlier this year after just 23 games at the helm.
Alonso has previously coached Real Madrid and Bayer Leverkusen.
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