Kroos worked with Guardiola at Bayern Munich.
"During my year with Pep Guardiola I took a big step forward," said the Germany international.
"Jupp (Heynckes) was the most important coach in the early stages of my career, both in Leverkusen and Munich. He saw me as a central player in his system, where my style of play fit perfectly."
On Real, Kroos added: "When you move to a top team abroad and affirm your position in the team, you've taken another step forward."