The Croatia midfielder made the move to La Real from RB Salzburg on Thursday.
Sucic said: "My feelings are fantastic, I am happy to be with the team. I already know the team and the people at the club, which is fantastic, I immediately noticed the quality of the players, the team and the club.
"The conditions here are excellent and the team is at its best level. I am very happy to be part of this team and looking forward to getting started."
He also said: "When you see which players have played for Real and those who are playing, you can only be happy to be here. I hope we can play very good football and win a title. We have to be a team that is very difficult to play against because, if we achieve it and we don't have injuries, we can have good results."