The Hammers made no secret of their desire to add a marquee forward to their front line this summer and signed Zaza on a season-long loan deal from Juventus last week.
"He's got everything on paper, of course," Bilic told the club's official website.
"Maybe he's going to need a little bit of time to adjust but we're going to help him.
"It's not an individual sport, don't get me wrong. One player can't change by himself.
"But we are expecting a lot from him."