City reportedly wanted a permanent move for Sinclair while Albion were keen on a loan deal for the 24-year-old.
However, the two clubs have now found a compromise with Sinclair expected to move to The Hawthorns on an initial season-long loan deal with an option to join full time next summer.
Sinclair started out with Bristol Rovers as a teenager and joined Chelsea in 2005, where he was loaned out to Plymouth, QPR, Charlton, Crystal Palace, Birmingham and Wigan.
The England youth player was signed by Swansea in 2010 and was then snapped up by City on transfer deadline day last summer but made only two league starts in 12 months under then boss Roberto Mancini.
Albion defender Liam Ridgewell played alongside Sinclair while the pair were both at St Andrews.
"Scott came on loan for a season and then he signed for Swansea that summer," said Ridgewell in the Birmingham Mail. "He is very quick and very direct and a very good player.
"He had grown up quite a bit from Blues through playing a bit and developed into a really good player," added Ridgewell.
"It would be great to have him down here."