Odegaard signed for Vitesse this week on a season-long loan.
"I have experienced the whole preseason at Real Madrid and I also got some playing time in matches against good opponents. It was a nice experience," he said.
"I feel good at Real Madrid. They really care about me and I trust that they want to keep me to the contract, which runs until mid-2021."
Vitesse coach Leonid Slutsky commented: "He is a big player. For us he is an ideal acquisition, because we were looking for a replacement for Mason Mount and Martin Ödegaard is a similar type of player. He is also a player who has creativity in his game."