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Real Madrid said on its official website that the 55-year-old Chilean had agreed to a two-year contract with the 31-time Spanish champions, and will be presented to the media on Tuesday.
Real did not reveal how much they have paid Villarreal - where Pellegrini was under contract until 2010.
Pellegrini has guided Villarreal to a fifth-placed finish this season. He took them into the Champions League twice in his five-year spell at the "Yellow Submarine", reaching the semifinals in 2006 and the quarter-finals this season, losing to Arsenal on both occasions.
Pellegrini will take over from Juande Ramos, who guided Real to second place this season, nine points behind all-conquering champions Barcelona.
Earlier on Monday, Florentino Perez assumed the presidency of Real, because none of the other candidates for the post had managed to give bank guarantees for 15 per cent of the club's budget, as the rules of the club stipulate.
Perez - who was president from 2000 to 2006 - announced that three former Real stars will be working with him: Jorge Valdano as general director, Miguel Pardeza as sporting director and Zinedine Zidane as special advisor to the president.