The Germany international arrived at Real in the close-season from Bayern Munich, with Alonso going in the opposite direction soon after.
Alonso had been at the club for five years following his switch from Liverpool and won La Liga, the UEFA Champions League and the Copa del Rey during his time with the club.
However, with Kroos in impressive form alongside Luka Modric for Real this term, Ancelotti believes the 24-year-old has proven his capabilities to replace Alonso - dubbed 'professor' by the Italian.
"He's another professor," Ancelotti is quoted as telling Spanish radio station Onda Cero.
"He has aced his crash course in replacing Xabi Alonso. I've been surprised by the fact that he never gets on edge. He always plays the same way, whatever the pressure.
"He's very important - a lot of our play goes through him. What's more, he's still very young. He plays at pace, always picks the right pass, doesn't lose the ball and wins back possession."
Kroos was one of a host of arrivals at the club this term, with James Rodriguez another star name to bolster Ancelotti's options following their European success last term.
With Angel Di Maria having left for Manchester United in the close-season, Ancelotti warned of comparing the two players.
"People should think twice before saying that James can fill Di Maria's boots, because they're very different players," he added.
"Di Maria could take matches by storm with his energy, but he also used to lose control sometimes, misplacing important passes."
