Sakho arrives at Upton Park from newly promoted Ligue 1 club Metz on a four-year deal for an undisclosed fee.
The 24-year-old Senegal international, who was named the best player in France's second tier last season after scoring 20 goals, is the third striker to join West Ham in the close-season following the captures of Mauro Zarate and Enner Valencia.
Sakho, Zarate and Valencia will be required to fill the void left by the injured Andy Carroll, who is expected to be out until late November after undergoing ankle surgery last month.
"This is a proud day to have signed for West Ham, I really love English football and I've dreamed of coming to play for one of the big English clubs," Sakho told the club's official website.
"West Ham have given me that opportunity and I didn't hesitate to grab it.
"I'm looking forward to playing. It's more than a month now that I've been training for this and right now I think I'd be ready to pull on the club colours.
"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."
West Ham - who get their Premier League campaign underway at home to Tottenham on Saturday - have also signed Cheikhou Kouyate, Aaron Cresswell, Diego Poyet and Carl Jenkinson on loan in this transfer window.
