Later on Tuesday Dortmund named Bellingham in their squad, external for the Club World Cup, which begins on Sunday.
Dortmund’s opening group game is against Brazilian side Fluminense on 17 June at 17:00 BST.
Bellingham had been named in the England squad for the European Under-21 Championship, to be held in Slovakia from 11-28 June.
But head coach Lee Carsley had said he would release players so they can compete at the Club World Cup in the United States.
Bellingham is following in the footsteps of older brother Jude by moving to the Bundesliga, as the England midfielder – who also came through the Birmingham City youth system – spent three years with Dortmund before joining Real Madrid in 2023.
He added in his farewell to Sunderland fans: “I hope that I have made you proud along the way, and in return, you have made me the player that has reached the heights I find myself at today.
“I will love and remember you fondly for the rest of my life.”
Dortmund, who have won eight German league titles, secured Champions League qualification by finishing fourth in the Bundesliga last season.
