Valencia agreed to join the Hammers from Mexican side Pachuca earlier this month but the signing was delayed until a hearing into his request for a permit.
Record signing Andy Carroll has been ruled out for four months following surgery on an ankle injury so Valencia's successful hearing means the 25-year-old now joins Carlton Cole, Modibo Maiga and new recruit Mauro Zarate in the Hammers' strikeforce.
Despite completing the capture of Valencia, who joins on a five-year deal for an undisclosed fee, manager Sam Allardyce is still likely to try and sign another forward with question marks remaining over Carroll's long-term fitness.
Valencia told the club's website: "It's exciting to be here in England and London.
"I want to repay the club in my performances for what they are investing in me and I'm really looking forward to it. I really appreciate the welcome I've been given and I'm excited to be here.
"I've already watched and read a lot about the club to learn about it - I know the fans are really passionate and I'm really glad to have signed.
"The World Cup was a good tournament for me personally, I scored three times and for my first World Cup it was a good experience, but I hope my next one is better for me and the team.
"Of course, the World Cup gives me confidence to come to Europe and I want to take and advance with this opportunity that West Ham have given to me."
Valencia also scored in Ecuador's 2-2 World Cup warm-up draw against England and wants to be just as successful when he comes up against the same opposition on a weekly basis.
"For me, scoring against England, one of the big teams in the world, before the World Cup was important. Hopefully I can score again against those defenders," he said.
"The Premier League is the top league and I have followed it in Mexico. Obviously my countryman Antonio Valencia has played here for a long time so it's a big step for me to come here from Mexico and I hope I can be as successful as Antonio.
"I scored many goals as a striker. I'm fast, and I try to continue like that because I know the goals brought me to West Ham."