The 24-year-old arrives at Upton Park after a successful two years at Sochaux in which he scored 24 goals in 59 Ligue 1 appearances.
The Hammers, who are back in the Premier League after winning promotion at the first time of asking via the play-offs, have not disclosed the fee paid for the six-foot-one striker who can also play in a wide role.
"I am really happy and excited about joining West Ham United,"Maiga told the club's official website. "I know West Ham are a big club in England and I'm really looking forward to representing them. They have huge tradition and it is like joining part of a family and that is one of the main reasons I wanted to come here.
"I know some of the big names that have played for the club in the past and I am proud to be part of a new team back in the Premier League."
Last summer Sochaux asked FIFA to intervene after claiming Newcastle United made an illegal approach for Maiga, but nothing came of it.
Maiga becomes the fifth major signing made by manager Sam Allardyce this summer. Goalkeepers Jussi Jaaskelainen and Stephen Henderson, defender George McCartney and midfielder Mohamed Diame have also all been signed since the end of last season.