Watt made his Blues debut in the FA Cup third round win over Scunthorpe last season, and is rated highly at Stamford Bridge.
He has spent time on loan at Barnsley, and will spent the next 18 months at the Liberty Stadium.
Swans boss Kenny Jackett said: "Steve is a quality player, he is strong in the air and in the tackle.
"In fact, his all-round game is very good. I am delighted to add him to my squad, he is a quality acquisition."