The Swans announced on their official website that they had agreed terms with Graham – last season's top scorer in the Championship.
Graham has agreed a four year deal at the Liberty Stadium with Watford also receiving a 15% sell on clause from any profit they make on a future sale of Graham.
"We have agreed all personal terms with Danny,'' explained Chairman Huw Jenkins. "He will have a medical and complete all the formalities once he returns from his holiday.
"Danny has also spoken to 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.''
