Carvalho completed a £6.7million move from Barclays Premier League champions Chelsea after passing a medical in the Spanish capital.
The Portugal defender becomes the fifth summer signing for Los Blancos, who have also added Sami Khedira, Pedro Leon, Angel di Maria and Sergio Canales to their ranks as manager Jose Mourinho looks to wrest the Spanish title from bitter rivals Barcelona in his first season in charge.
Real, who finished second in La Liga under former manager Manuel Pellegrini last season, have been linked with a move for Germany star Mesut Ozil while squad players like Lassana Diarra could move on thanks to this summer's influx of players.
"We are comfortable with the team that we have, but the exits and arrivals might not be over," Valdano told reporters at Carvalho's unveiling.
Valdano revealed that Mourinho is looking for add an attacking player to his squad before the transfer window shuts and while Ozil fits the bill perfectly, the Real general manager refused to confirm whether the Werder Bremen man was on Mourinho's radar.
He added: "There could be new signings and the club are open to all different possibilities but I can't name more possibilities in regards to who."