Bayern ended months of speculation that Lewandowski will follow former Dortmund team-mate Mario Gotze to the Allianz Arena by announcing on Saturday that the striker will join on a free transfer at the end of the season.
Klopp has welcomed the end of the saga and is pragmatic about the 25-year-old's departure, explaining that he is not surprised to lose the Bundesliga's top scorer to the German and European champions.
And Klopp is also hopeful that Lewandowski will now finish with a flurry of goals and match-winning performances before leaving as Dortmund sit fourth, 12 points behind Bayern.
"Well I have spoke with Lewy just before end of last year and I knew it would happen in the early days of January," he said
"I also believe it's the best time to let it happen, otherwise there would have plenty of unnecessary rumours all the time. That doesn't bother us anyhow, so it's good the way it is.
"It wasn't a problem, I mean we could draw some scenarios or whatever, but seriously we knew for such a long time now that Robert would play for a different club after the summer.
"Other than that nothing will change. Since then I have noticed that he is showing less interest in us and had been straying away from our focus.
"He took the winter break to tackle these issues, it made sense and now he is focusing on Borussia Dortmund again. That's the way it is, he will be somewhere else from summer onwards.
"Until then we want to make this very important remaining half year with him as profitable as possible."
Klopp went on to say he is in no rush to find a replacement for the Poland striker.
He added: "I don't think it is useful to speak about this (replacing Lewandowski) now.
"The main question is what we can afford and who is available, and which player is at a stage of his career where he is willing to join us on our journey, the direction we want to go as a club.
"We have been searching for such a long time already for a replacement, it's not a surprise is it?"
