The 27-year-old will complete his move to the Championship club on an emergency basis when the loan window opens on Saturday after finding opportunities limited in Wales
Lita has completed a medical with the Championship club and will now wait for the move to be ratified when the loan window opens on Saturday.
Blues manager Lee Clark has previously worked with the 27-year-old and expected him to add "power and pace" to the club's forward line.
"I know Leroy very well having worked with him at Norwich during a loan spell in which he scored seven goals in 16 games," Clark told the club's official website.
"He's a proven goalscorer who has power and pace and there's no doubt that he'll add quality to my squad."
Lita joined Swansea shortly after they were promoted to the Premier League in July 2011 from Middlesbrough. He has since made only 16 Premier League appearances for the Welsh club, however, scoring two goals.
The Zaire-born player made his name with Bristol City before helping Reading to promotion to the top flight as the club's record £1 million signing.