The 42-year-old Italian, who spent a glittering seven-year spell with Chelsea during his playing career, signed a three-year contract with the Hammers.
"It is a great club and I couldn't have said no. I'm very pleased to have accepted it. It's a great opportunity and I'm sure I can do a good job," he told a press conference.
"This club is ambitious and I am ambitious too. I want to get better and better…ambition is very important to me.
"As long as you work hard and you know what you are doing you will be fine."
Zola, who becomes West Ham's first ever foreign coach, succeeds Alan Curbishley, who resigned from his post due to the board's interference in his job.
The West Ham job will be Zola's first ever coaching role, as his only experience was working as an assistant to Italy U21 coach Pierluigi Casiraghi.