The two clubs reportedly agreed a fee for the South Korea international earlier this week, thought to be around £6m.
Ki is looking forward to the "honour" of playing in such a prestigious league, and is keen adapt to the new style of play as quickly as possible.
"It's an honour to play in such a world-class league that I've only watched on television," the 23-year-old told Yonhap.
"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."
If the deal is done in time, Ki could make his debut in Swansea's match against West Ham United on Saturday.