The move coincides with the appointment of new president, Florentino Perez, who arrives at the Santiago Bernabeu for a second time with Zinedine Zidane as an advisor.
Perez has already indicated that AC Milan's Brazilian playmaker Kaka is the number one player target for the nine-time European champions.
Real have also been strongly linked to Manchester United forward Cristiano Ronaldo, Liverpool's midfielder Xabi Alonso and Bayern Munich's winger Franck Ribery.
Pellegrini's switch from the 'Yellow Submarine' is seen as a major step to bring some much-needed stability to the Spanish giants, after bitter rivals Barcelona won the Copa del Rey, La Liga and the Champions League.
Since coach Vicente del Bosque was sacked by Perez in 2003 after winning two Champions Leagues and two league titles, the club have seen Carlos Queiroz, Jose Antonio Camacho, Mariana Garcia Remon, Wanderley Luxemburgo, Juan Ramon Lopez Caro, Fabio Capello, Schuster and Ramos come and go.
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