The Premier League new boys have paid a club-record £3.5million for the 25-year-old striker.
Graham has agreed to a four-year contract with Swansea.
A Swansea statement read: “The club has today agreed personal terms with Watford striker Danny Graham. Graham will sign a four-year contract with an additional 15% sell-on clause to Watford on any profit above the £3.5million.”
Swans chairman Huw Jenkins added on the club’s website: “Danny has also spoken to [Swans manager] Brendan Rodgers at length. He is thrilled to conclude the deal and is looking forward to the challenge of Premier League football with Swansea.
“He is a player we have admired for quite some time and as a football club we are delighted to get our man. Brendan is looking forward to working with him and there is no doubt he will strengthen our team for the new campaign.”
