The South Korea international has been a long-term target for the Premier League club, after impressing for the SPL side since joining in 2010 with his performances prompting reported interest from Arsenal.
Ki, who becomes the most expensive player South Korean football history following the move with the fee a reported £5 million, revealed that the club's philosophy attracted him to the Swans.
“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.
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“It was very impressive, and I think I can grow as a player here and help the club move forward.
“The manager 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.”
As exclusively revealed by Goal.com earlier on Friday, Laudrup is keen to add further new faces to his squad at the Liberty Stadium with Pablo Hernandez of Valencia, Tom Ince of Blackpool and Bristol City’s Albert Adomah all interesting the Dane.
And chairman Huw Jenkins confirmed that the arrival of Ki was possible due to the sale of influential midfielder Joe Allen to Liverpool.
Jenkins added: "Having lost Joe Allen recently, it was vital that we invested the money wisely by bringing quality young footballers into the club with potential to grow further.
"Ki fulfils that criteria and everyone in the football club is excited about the prospect of him playing and developing with us."