Gundogan, 26, returned to action in midweek against Girona after eight months of hell coming back from torn knee ligaments suffered last December.
He said: “The city is starting to feel like home. I enjoyed the time that I spent in Germany – I won a lot of trophies and appreciated my time there.
“But it was the right time to move on and try something new. When I had the opportunity to join City I wasn't afraid of it for one second.
“I live in the city centre so being there and being able to go out to a restaurant, or some bars, or to have a coffee somewhere is great. Everyone is friendly to me – even United supporters.
“There's a lot for me to look forward to over the next few months and it's really exciting. Hopefully it will be a good year for me."