The two clubs have reportedly agreed a £1.75million fee for the 26-year old and now he just needs to pass the medical test before he is reunited with former Reading boss Brendan Rodgers.
"Leroy is a proven goalscorer. It would be a fantastic deal for this club," Rodgers told the club's official website.
"Our supporters would love him because he is a player that is loved by the supporters of every team he plays for.''
Swans chairman Huw Jenkins added: "Myself and Brendan are delighted to come to an agreement with Leroy.
"As I have said previously, Leroy was one of the manager's main targets when he arrived in Swansea a year ago.''