The 24-year-old Senegal international has moved to Upton Park after agreeing a four-year contract.
His 43 goals over the last two seasons helped Metz win back-to-back promotions into France's Ligue 1.
Sakho is the third striker to join the Hammers this summer, following the arrivals of Argentine Mauro Zarate and Ecuador international Enner Valencia.
Sakho told the club's West Ham TV: "I really love English football and I've dreamed of coming to play for one of the big English clubs. Today, West Ham have given me that opportunity and I didn't hesitate to grab it.
"I've come here to continue as I was at Metz. I'm going to give it my all, going flat out on the pitch and I think the fans will appreciate that."
Manager Sam Allardyce, meanwhile, has backed a club statement that the team's approach needs to be more entertaining.
Former Millwall, Tottenham, Manchester United, West Ham and England striker Teddy Sheringham has been brought in as an attacking coach.
West Ham have signed striker Diafra Sakho from French side FC Metz for an undisclosed fee.