Valencia's successful work-permit hearing means the 25-year-old now joins Carlton Cole, Modibo Maiga and fellow new recruit Mauro Zarate in the Hammers' strike-force, with the former Pachuca man looking to build on an impressive World Cup in which he scored all three of Ecuador's goals.
"It's exciting to be here in England and London," he told West Ham TV.
"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.
"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."
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