The Japan international struggled to impress at Manchester United following his move from Signal Iduna Park two years ago and he returned to BVB in a cut-price deal late in the summer transfer window.
Following Kagawa's return for Jurgen Klopp's men on Saturday, in which he starred and scored as Dortmund defeated Freiburg 3-1, Grosskreutz is thrilled to have his "good friend" back at the Bundesliga club.
"The most important thing to take away from the clash with Freiburg was that we won," the left midfielder told Ruhr Nachrichten. "It's true, though, I get along great on and off the pitch with Kagawa.
"We are good friends and stayed in regular contact when he joined Manchester United. We are strong together as we showed against Freiburg.
"He is technically superior to others, he can sometimes take on two or three players on his own. It is great fun playing alongside him."
Kagawa is expected to feature again on Tuesday when Dortmund begin 2014-15's Champions League campaign against Arsenal and Grosskreutz is particularly looking forward to clashing with Germany compatriot Lukas Podolski.
"Of course I'm looking forward to facing Poldi," the World Cup 2014 winner laughed. "It'll be an exciting duel. Poldi, watch out, I'm coming for you!"
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