The Serb joined Hertha on a straight season-long loan yesterday.
Grujic said: "I am very happy that it worked out with the transfer. Hertha BSC is a big club and I've always loved the Bundesliga. I have had a few offers, but no one has been as serious with me as Hertha.
"I immediately had a very good feeling during the talks. Now I want to show as quickly as possible that I can help the team."
Hertha chief Michael Preetz also remarked: "With Marko, we got exactly the type of player for the central midfield we were looking for. He is technically strong and fits perfectly with our defensive and offensive qualities, his physique in a duel and his good heading plays into our profile."