The 24-year-old has put pen to paper on a deal that runs until 2031 after leaving Dortmund with one year remaining on his contract.
Barcelona are understood to have agreed an initial transfer fee of 22 million euros, with the deal potentially rising to 31 million euros through performance-related bonuses. Dortmund have also secured a sell-on clause that could see them benefit from any future transfer.
Adeyemi leaves the Bundesliga club after four seasons, during which he established himself as one of Dortmund's key attacking players and earned 11 caps for Germany.
Dortmund sporting CEO Lars Ricken said the club respected the player's desire to make the move.
"Karim has been an important part of Borussia Dortmund over the past four years. When Karim approached us with his wish to move to FC Barcelona, we agreed to it after weighing all the interests of Borussia Dortmund."
Speaking after completing the transfer, Adeyemi admitted joining Barcelona was the fulfilment of a lifelong ambition.
"It's difficult to put into words because this is something I've dreamed about since I was a kid. I've told my dad that one day I would play for this club."
The German forward also said he is looking forward to working under head coach Hansi Flick and playing alongside some of Barcelona's brightest talents.
"Lionel Messi has always been one of my idols. I'm excited to play alongside players like Lamine Yamal and Pedri. This club represents excellence, ambition and winning."