Rafael Benitez's Real have been heavily linked with a move for the Spain international and were reported to be in advanced negotiations with Casilla on Thursday.
And the 28-year-old is poised to make the move to the Santiago Bernabeu after Espanyol confirmed that a deal had been finalised.
Casilla said: "It was a unique opportunity and one I had to take. I am very grateful to Espanyol for all they have done."
The transfer comes five days after Real legend Iker Casillas ended his 25-year association with the club by agreeing to a two-year deal with Portuguese side Porto.
Real had been expected to try to sign David de Gea from Manchester United to be their number one goalkeeper following Casillas' exit.
It remains to be seen whether Real will still pursue De Gea on the back of the signing of Casilla, who adds to a Real side already bolstered by the arrival of Danilo and Marco Asensio – who both agreed to deals last season – and Lucas Vazquez for the new campaign.
Casilla joins Keylor Navas and Fernando Pacheco as the three goalkeepers in Real's squad.