Alex, 31, joins on a free transfer after his contract with the French champions expired last month and revealed Silva - who was a Rossoneri player before playing with Alex in Paris - played a role in his decision to move to Italy.
"We have talked much about Milan together, the talks were long,” said Alex. “Thiago Silva always spoke well of this team and the environment.”
With new coach Filippo Inzaghi tasked with improving Milan's eighth-placed finish in Serie A last term, Alex feels he can play a part in strengthening their defensive ranks.
Milan shipped 49 goals last term but, in his first foray into Italian football, Alex wants to help repay fans for the welcome he has received.
"This season we will put in a lot of effort, while the fans will support us. Yesterday [at the pre-season launch at Casa Milan] it gave me chills throughout the reception," he said.
"We will work hard to repay all this affection [and] I am sure I can lend an important hand to the team, I will bring to them my experience.
"With work and commitment we will also fight for the Scudetto. Tactically, we are already working on avoiding conceding these goals.”