Zapata is Milan's first significant signing of the summer.
"I accepted Milan because they are a great side who always fight to win," said the Colombian in today's Press conference.
"Being Thiago Silva's 'heir' does not weigh on me. I'm not remotely frightened of the pressure that comes with that. I'm here to prove I am worthy of Milan.
"I realise Milan have lost two of the best centre-backs in the world, but I know I'm a good player and if I work hard then I can do well.
"I still haven't spoken to Mario Yepes, as he is on international duty, but I already partnered him in defence for Colombia and hope to do the same here.
"I am a centre-back, but if it's needed then I can also play on the right. I struggled at Villarreal because it was a whole new League and they immediately put me on the right, so I struggled to adapt.
"I played for six years in Italy and I'm happy to be back 'home.' The transfer all happened very quickly. As soon as I knew Milan were interested, I couldn't wait to start training at Milanello."