The 22-year-old Borussia Monchengladbach and Germany forward, who has scored 10 goals this season, agreed last week to join Dortmund at the end of the season in a five-year deal that is the biggest so far in the winter transfer period.
"Dortmund have been successful in keeping up with their own understated position," Bayern sports director Christian Nerlinger told Bild newspaper. "This is now finished with this transfer. It is a whole new step."
Bayern coach Jupp Heynckes said Bayern had had a string of rivals over the years but remained top of the heap as challenges from clubs such as Werder Bremen, Gladbach and Dortmund faded after a few seasons.
"Let's wait and see how long they can keep moving on this level," Heynckes told reporters.
Dortmund, surprisingly dominant champions last season and in second place three points behind Bayern in the current campaign, have repeatedly played down their chances of defending the title, saying they would be happy with a finish that would secure them European football next season.
"Have no fear. When we decide to change our strategy we will make sure to let Mr Nerlinger know," Dortmund coach Jurgen Klopp told reporters in response.
The 1997 Champions League winners have come back from the brink of financial ruin a few years ago to become Bayern's biggest title rivals in recent seasons.
Reus's reported 17-million-euro transfer only underlines their ambition for a more permanent place at the top of the Bundesliga.
