The midfielder will spend the rest of the season on loan at Dortmund from Tottenham Hotspur.
The German side has an option to make the deal permanent in the summer.
“I am very happy to be at Dortmund and glad that I have left Spurs,” Boateng told Bild. “I definitely wanted to go back to the Bundesliga.
“Three days ago my agent phoned me to prepare myself for a transfer, but a few hours later the deal seemed off.
“But then I got in touch with (chairman) Daniel Levy and requested a transfer. He agreed!
“I have made a lot of mistakes in my career, but I feel I have acquired maturity during my difficult spell at Spurs. I had more than enough time to think about doing better.
“Borussia is lying in sixth actually and still has every chance to go to Europe next season. I want to help them to reach that.”