"It's difficult to say how I happy I am because it's not easy to get top-class players," Poyet told Brighton's official website.
"I'm absolutely delighted to have Wayne with us. He's been one of the top three left-backs in this country for many years.
"There were a lot of things that had to come together to make it happen. Firstly, David Platt has been great at Manchester City and then Wayne and his agent have helped a lot too.
"It was not an easy one to secure, but this is what we want at this club. He's a quality player with lots of international experience.
"Wayne has played at the top of English football for a long time. We have all got to learn from him and I'm sure that he will have a very good season with us. It's going to be very nice to sit back and watch him on the pitch."