The goalkeeper has no resentment towards the club despite appearing to have been forced out of the Santiago Bernabeu following the arrival of Keylor Navas
The Spaniard began his career at the club before returning from Sevilla in January 2013, as Jose Mourinho installed him as his first choice goalkeeper ahead of club captain Iker Casillas.
He then shared duties with his compatriot last term, only to see Costa Rica star Keylor Navas join Madrid from Levante, a move which has forced him out of the club.
Goal reported last week how the 32-year-old got into a row with officials after learning of their desire to sell him, though he insists he bears no resentment towards his soon to be former employers.
He told reporters on Monday:"It was a very happy time in my life and I can only thank Madrid. I am very pleased to be joining a club like Milan.
"I hope to close my transfer tomorrow and there is no problem in the medical examination."
Lopez is expected to arrive in Milan on Monday evening before undergoing a medical on Tuesday.