As a player between 1996 and 2003 at Stamford Bridge, Zola won five major trophies including the FA Cup twice.
"For me it is an amazing thing. I am pleased to be here," said Zola.
"It would be great to be successful with Maurizio and for the club and I will give my best, as I did in the past as a player.
"I am very much looking forward to the challenge in general. I would love us to start well and we are all very excited to start this new adventure."
Italian Zola made 312 league and cup appearances for Chelsea, scoring 80 times.
Sarri replaces compatriot Antonio Conte, who was sacked despite winning FA Cup and Premier League titles.