Dortmund will receive a transfer fee of 22 million euros (£18.8m), which could rise to 31 million euros (£26.4m)with bonuses. BVB is also set to benefit from any potential future sale.
According to media reports, Adeyemi's salary will be six million euros (£5m) per year.
"Karim has been an important part of Borussia Dortmund over the past four years," Dortmund's sporting CEO Lars Ricken said.
"When Karim approached us with his wish to move to FC Barcelona, we agreed to it after weighing all the interests of Borussia Dortmund."