The South Korea international has signed a three-year contract at the Liberty Stadium but will not be available for Saturday's clash with West Ham.
Ki told swanseacity.net: "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."
Ki revealed the Swans' style of play and the presence of Michael Laudrup as manager both played a part in enticing him to make the move south.
"When I look at Swansea I see a club that is growing and growing, and the style here is very attractive to me," he said."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 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."
Swansea chairman Huw 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."
Ki spent two and a half years at Celtic after signing from FC Seoul in January 2010, the highlight of which was a goalscoring, man-of-the-match performance in the 2011 Scottish Cup final against Motherwell.
He came up against new team-mates Neil Taylor and Scott Sinclair, as well as Allen, when his side beat Great Britain on penalties in the recent Olympic tournament, with Ki scoring the first spot-kick.
He also has experience of the Liberty Stadium after a pre-season friendly with his former club and said: "I remember playing here for Celtic and the fans here made a lot of noise. This is a lovely stadium. I can't wait to get out there and be a part of the team. But first I will enjoy watching the game on Saturday."
Source: PA
Source: PA