The Swans had already negotiated a £1.75 million ($2.8 million) transfer fee with Middlesbrough earlier in the week and, despite reported interest from Leicester, Lita appears set to move to the Liberty Stadium.
The 26-year-old now has to pass a medical in south Wales before officially completing his move to a team looking forward to their first top-flight campaign for 28 years after last season's Championship play-off final victory over Reading.
Swansea boss Brendan Rodgers, who worked with Lita at Reading, said: "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: AFP
Source: AFP