The 21-year-old Germany international switched to the Allianz Arena in the off-season for 37 million euros and scored his first Bundesliga goal for the Bavarians as they came from behind to win 3-2 over Hertha Berlin on Saturday.
Gotze said joining a Bundesliga rival was no problem for him, all the while battling to recover from a hamstring in preseason.
"Getting through the rehabilitation period certainly wasn't easy but I was pretty sure I would settle into the side and surroundings quickly here," he told Bundesliga.com. "I already knew a few players from the national team and I think that's helped make everything easier for me.
"I'm just happy to be playing for Bayern now, with the coach and all the other stuff...that was a really important part of why I moved here."
Gotze conceded he was fortunate to get on the score sheet and give his side what would turn out to be a necessary two-goal buffer as Hertha pulled one back late on.
"It was pretty lucky the way it dropped in at the back post," he said. "There wasn't much power on the header but thankfully it went in. Lucky but good for us."
Gotze also heaped praise on fifth-placed Hertha for a brave performance in Bavaria, as the newly promoted club threatened to cause a shock before eventual defeat
"It was a tough game," Gotze said. "We were up against a really aggressive, on form, Hertha side. They're not where they are on the table for nothing."
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