The highly-rated German joined Los Blancos in a €25 million (R360 million) move from the Bundesliga champions, and has been a mainstay in a star-studded Galactico midfield, featuring in all seven La Liga fixtures and two Champions league fixtures thus far this season.
"I've settled in very well in a very short space of time,” Kroos told reporters.
“I feel very integrated, both within the team and outside it.”
The 24-year-old admitted he has yet to learn Spanish due to the busy match schedule with his new club, but reveals he is able to communicate in English with various members of the squad.
"I started having a game almost every four days as soon as I arrived so I haven't had much time,” he said. “I'm trying to learn the language bit by bit which will help me in my relationship with the team. At the moment I'm doing ok with English.”
Kroos has been compared with former Real midfielder Xabi Alonso, who went the other way in a move to Bayern, yet Kroos says he does not wish to be compared to the former stalwart in the Madrid midfield.
"I don't like comparisons," he said.
"We're not such different players if you consider the position we both play.”
Kroos then spoke of the level of football in Spain compared to that of the Bundesliga, saying that smaller teams are more committed, yet pose less of a threat in La Liga than in Germany.
"They show more commitment than in the Bundesliga,” he said. “I think that, in general, there are better players in La Liga than in the Bundesliga, although in Germany there are more teams that pose more difficulties."
Kroos is currently on international duty with Germany, who face Poland and the Republic of Ireland in their upcoming Euro 2016 qualifiers this week.