Lita has signed a three-year contract with the Welsh club after a deal worth ?£1.75 million ($2.8 million) was agreed with Middlesbrough last week.
He could now make his first Swansea appearance in a friendly against Celtic later Wednesday.
A statement on the Swansea website read: "Swansea City are pleased to confirm they have completed the signing of striker Leroy Lita after he passed a medical today (Wednesday)."
Swans manager Brendan Rodgers has been busy strengthening his squad ahead of the club's first season in the top-flight for 28 years and had already signed Danny Graham, Steven Caulker and Jose Moreira.
Source: AFP
Source: AFP