The 23-year old South Korean international has joined the Swans for a club record fee, believed to be in the region of £6million.
Ki, who has signed a three-year deal with the Swans, is looking forward to adapting to life in Wales with a very exciting squad at the Liberty Stadium.
"When I look at Swansea I see a club that is growing and growing, and the style here is very attractive to me," he told the club's official website.
"Last year I watched them a lot in the Premier League and they did things very differently to a lot of the other teams. They wanted to keep the ball and pass it around, which I love to do. When they didn't have the ball they worked so hard to get it back quickly.
"It was very impressive, and I think I can grow as a player here and help the club move forward.
"The manager (Michael Laudrup) is another big attraction. I remember watching him when I was younger and I was amazed by how good he was.
"Now I want to learn from him in order to help me become a better player. I learned a lot at Celtic - it helped me become more of an all-round player.
"This is something I have dreamt about since I was a child - playing in the Premier League against the best players in the world. I can't wait to play my first game."