The Ukraine winger, 28, joins the Hammers on a four-year deal for a reported fee of £17.5million.
Yarmolenko underwent a medical at West Ham's pre-season camp in Switzerland earlier this week.
He said: "West Ham is a big club with good fans and I am happy to come to play in the Premier League.
"The Premier League is the best league in the world and I know that an interesting project is being built here at West Ham. The team wants to achieve high things and I am excited for this challenge."
Yarmolenko, who has 77 Ukraine caps, is new boss Manuel Pellegrini's fifth signing since taking over.
He joins Jack Wilshere, Ryan Fredericks, Lukasz Fabianski and Issa Diop through the doors at the London Stadium.
Irons director of football Mario Husillos said: "He really is the kind of player that we were looking for.
"He is a left-footed player but can play on the right and is very quick, very good one-on-one against a defender.
"He gives the team a lot of attacking options and scores goals, is fast on the counter-attack and provides aerial threat with his height.
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"He also has very good experience, of playing for big teams and fighting for titles. At Dortmund, he had some good matches but perhaps didn't quite show his very best.
"However, I think Manuel Pellegrini is the perfect coach for Andriy and his style of play.
"I believe he is joining us in the perfect moment.
"He is 28, the prime age for football, and we have great expectation about what he can achieve with West Ham United."
Yarmolenko began his carer in Ukraine with Desna Chernihiv before moving to giants Dynamo Kiev in 2008, where he spent nine years before signing for Dortmund.
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