Sinclair, 23, excelled in South Wales after struggling to make the breakthrough at Chelsea. He was an integral part of the side which earned promotion to the top flight in 2011 and also impressed on their opening season in the Barclays Premier League.
"I'm just glad everything is settled and that I'm now a City player," said Sinclair.
"There were times when I thought it might not happen so I'm relieved that I'm here and I can't wait to get started.
"Playing alongside some of the best players in the world is exciting for me and when you see two Champions League fixtures against Real Madrid on the horizon, it brings it all home."
Sinclair has had a busy summer after starring for Great Britain at the London 2012 Olympics, playing four times and scoring once.
Source: PA
Source: PA