The former Man City, West Ham, Q.P.R. and England winger passed his medical, signed his contract and then flew out to Portugal on Tuesday evening.
Sinclair has appeared in over 500 league games scoring over 70 goals. He has 12 England caps. His transfer value over three moves totals over £5m.
Sinclair is City's 5th summer signing joining Tony Capaldi, Gavin Rae, Steve MacClean and Michael Oakes.