PSG saw several bids for the commanding centre-half rebuffed last month and Milan have now convinced him his future lies with the Rossoneri.
Silva has signed a five-year deal which ties him to the club until June 2017.
The South American told the club's official website, www.acmilan.com: "I want to make history in Milan, like Franco Baresi and Paolo Maldini."
His decision to stay is a major coup for the club as they look to reclaim the Serie A crown they lost to Juventus last season.
Milan owner Silvio Berlusconi said: "Thiago Silva is staying at Milan."
A Milan statement added: "An important decision (has been) taken in difficult times and faced with a unique economic proposal.
"Thiago Silva is not simply a champion who tackles and wins back the ball, who, with his team-mates, wins, draws or loses the match. Thiago Silva himself embodies the class and style of Milan, the charisma of a club that loves the game but also the result and behaviour.
"And so his stay with the Rossoneri, decided by president Berlusconi, preserves the Milan identity."
Silva, 27, joined Milan from Fluminense in the summer of 2009 and has since developed into one Europe's most coveted defenders.