The Swans confirmed earlier this week they were in discussions with the 23-year-old and his representatives after reportedly agreeing a fee of around ?6million with Celtic.
Ki has followed English football with interest for some time and is looking forward to the challenge of playing at such a level.
Speaking to reporters at Incheon airport before flying to London, the South Korean was quoted by Yonhap as saying: "It's an honour to play in such a world-class league that I've only watched on television.
"The key is to make adjustments to my new environment as quickly as I can. If I can just play my game, I think I will have a good career there."
Ki has attracted the attention of other Premier League clubs and did not confirm he is about to join Swansea, but he has admitted he likes the Welsh team's playing style and praised manager Michael Laudrup.
"I would expect to learn a lot from him, since he was such an internationally renowned player."