The 27-year-old, who will wear the number nine shirt, has spent his entire professional career at Dynamo, making 339 appearances over the course of 11 seasons and scoring 137 goals.
"I'm very grateful that Dynamo Kiev have allowed me to fulfil my dream by moving to a big European club," he said in a statement on Dortmund's website. "I will work hard in training to help BVB reach their highest goals."
France international Dembele, who scored 10 goals and provided 20 assists in all competitions to help Dortmund finish third in the Bundesliga last season, was sold to Barcelona on Friday for 105 million euros ($125 million).
The deal's add-ons will make it the second most expensive transfer of all time.
Yarmolenko, who won three Ukrainian league titles with Dynamo, has made 69 appearances for Ukraine, scoring 29 goals.
"Andriy is a player we've been following for some time," said Dortmund's sporting director Michael Zorc.
(Writing by Brian Homewood, editing by Ed Osmond)
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