Milan confirmed the news via their club television channel on Saturday morning.
Lopez is expected to undergo a medical on Monday before penning a four-year deal in the Italian capital.
The 32-year-old's departure was seemingly hastened by Real's summer signing of Costa Rica star Keylor Navas from Levante.
Lopez shared the number one jersey with Iker Casillas following his arrival at Los Blancos midway through the 2012/13 season from Sevilla.