These are the two first changes made following the return for Florentino Perez as Real Madrid president.
Pellegrini will be officially unveiled at Santiago Bernabeu on Tuesday.
“Real Madrid and Manuel Pellegrini have reached a deal for the Chilean coach to be the first-team head coach during the forthcoming season,” read a statement on the club’s official website.
Jorge Valdano has been named director general and assistant to the president at Real while Miguel Pardeza takes over as the club’s new sporting director.
“We will devote all our effort to building a spectacular team, with great players who are role models on and off the pitch,” Perez said.
“A club where ethics are indestructible, and where solidarity will be a basic cornerstone of behaviour.
“The challenge that today begins for all of us is possibly the biggest and most difficult that we have ever taken on, but I assure you that we will make this Real Madrid a great symbol and example.
“We are going to rebuild and reassert the dreams of all Madridistas. We have a lot of work ahead. There is a lot to do, so let us begin.”