A fee of £1.75million for the former Reading man was agreed earlier in the week and, despite reported interest from Leicester, Lita has successfully negotiated personal terms with the Liberty Stadium club.
The 26-year-old will undergo a medical in south Wales next week before signing a three-year deal.
Swansea chairman Huw Jenkins said: "Myself and (manager) Brendan (Rodgers) 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.''
Lita is expected to come into contention for Wednesday night's friendly against Celtic.
Rodgers, who worked with Lita at Reading, added: "Leroy is a proven goalscorer.
"It would be a fantastic deal for this club.
"Our supporters would love him because he is a player that is loved by the supporters of every team he plays for.''
Source: PA
Source: PA