Shinji Kagawa accepts he failed to deliver at Manchester United but told Sport Bild: "My heart had remained at BVB."
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Kagawa re-signed for Borussia Dortmund at the end of last month after struggling to make an impact during his two years at Old Trafford under Sir Alex Ferguson and David Moyes.
Louis van Gaal took charge at United in the summer but made it clear Kagawa was free to leave after failing to buy into his "philosophy," and the Japan international said he was in no doubt as to his preferred destination.
"My decision was clear: I wanted to return to BVB and only to BVB," said Kagawa, who won two Bundesliga titles and the DFB-Pokal during his initial two-year stay at the Westfalenstadion. "I want to achieve success with this club again, and with no other."
Kagawa made 71 first-team appearances for United but, after showing promise during his debut campaign under Ferguson, he failed to register a single goal under Moyes last season.
"Only facts matter in football -- stats, goals, assists, titles -- and a lot was missing in this regard," he acknowledged. "That was probably why they no longer included me in their plans."
He added: "Everybody knows that my second year at Manchester United was particularly difficult. The manager did not really count on me, and the team was also on a bad run. That means I am all the more delighted to be back. My heart had remained at BVB anyway."
He declined to criticise Van Gaal, however, insisting it would be "unfair" to draw comparisons with BVB boss Jurgen Klopp. "I only worked under him for a month," he said.
Dortmund have not won a major trophy since Kagawa's exit in 2012, but he believes they remain serious contenders both in Germany and Europe.
"Fundamentally, I want to win everything -- that's my nature," said Kagawa, who scored on his return to action in a 3-1 win against Freiburg at the weekend. "We also have what we need -- the players and the coach -- to win titles.
"Having said that, we had that at Manchester and it didn't work. A lot of things have to click, but I hold the belief that this is absolutely possible here."
Bayern have dominated the Bundesliga in the last two seasons and Kagawa said: "Bayern have an unbelievable team with sensational players. We don't need to talk about that.
"They are a force, but it should our aspiration -- and also that of a few other Bundesliga teams -- to fight them with confidence and be able to beat them. We will do all we can for that."
Dortmund have put in some impressive performances so far this season despite missing key players like Marco Reus, Ilkay Gundogan and Mats Hummels through injury.
"The situation is difficult, but BVB has always had a team that is united and draws its strength from that," he said. "I am looking forward to the day when everyone's fit and we can bring all that quality to the pitch."