The former Genoa goalkeeper made the switch last night.
Martinez has signed a deal to 2029 and told Inter's website: "I am convinced that I am ready to make that big leap in quality. I know where I am, in the best club in Italy now. My mentality is that I come here to give the best of myself and try to make the history of the club bigger.
"I was really lucky to have been in the most important schools for goalkeepers: I was in Spain, Germany and now I'm in Italy. Taking a little from all these schools helped me grow. Playing at Barcelona, Las Palmas and Genoa there was the philosophy of wanting to be protagonists with the ball. This shapes your personality and your character.
"I'm very happy here, both in Serie A and in Italy. I like it a lot because it's a country similar to Spain. I know where I'm coming from, I know that the championship is very, very competitive. If we want to win the scudetto again, which is goal number one, we have to maintain last year's level."