The 25-year-old, who scored all three of Ecuador's World Cup goals in Brazil this summer, has put pen to paper on a reported five-year contract after agreeing personal terms and passing a medical.
Hammers manager Sam Allardyce beat off competition from several other Premier League clubs to sign Valencia, whose fee could equal the club record £15m paid for Andy Carroll.
He will become West Ham’s fifth signing of the summer, joining Argentine striker Mauro Zarate, centre-back or midfielder Cheikhou Kouyate, Ipswich Town left-back Aaron Cresswell and Charlton midfielder Diego Poyet at the club.
Valencia also caught the attention ahead of the World Cup when he scored a header for Ecuador in a 2-2 friendly draw with England in Miami, and prior to that he had netted 18 goals in 23 outings for his club.
West Ham winger Stewart Downing has already tipped Valencia to be a success alongside Zarate and Carroll at Upton Park.
He said: "For large parts of last season we played without a striker. We can't rely on Andy all season.
"He was the big signing last season, but Andy struggled with injuries so hopefully the new signings will take the pressure off him a little bit. And from what I've seen of Valencia against England, he looks a very good player.
"He can nick a goal and it is competition for places. It's what we've needed as we didn't have that last season. It will help the manager that he has options and he can bring other people in who can perform straight away."