The Hammers have been in talks with the German club for the past few days, and have finally reached a breakthrough, securing the Ukraine global for a fee of £17.5 million (€20m/$23m).
Yarmolenko will become the seventh Ukrainian to play in the Premier League.
A near-constant in the gossip columns for the past four or five years at least, the Ukranian has finally arrived in the Premier League - moving to the Hammers from Borussia Dortmund for the princely sum of £17.5million.
As for arrivals, Achraf Hakimi is set to join on a two year loan deal.
The 28-year-old is still capable of producing moments of brilliance, as he showed with his six goals and six assists in all competitions last season.
And he was clearly delighted to wrap up the move, saying: "Of course, I am very happy to sign for West Ham United".
"We are very happy to welcome Andriy", West Ham director of football Mario Husillos said in a statement.
'The team wants to achieve high things and I am excited for this challenge'. West Ham hope to follow the signing with the £40m capture of Lazio midfielder Felipe Anderson.