The former Chelsea winger has expressed his relief at finally sealing a move to the Premier League champions following a summer-long chase from Roberto Mancini
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The 23-year-old, who played four times for Great Britain this summer at the London 2012 Olympics, could be in line for his debut in the game against QPR on Saturday.
Goal.com exclusively revealed the Premier League champions' interest in the former Chelsea man on August 8 and, after protracted negotiations, a deal has been finalised.
"I'm just glad everything is settled and that I'm now a City player," Sinclair told the club's official website.
"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 is Roberto Mancini's third summer signing after Jack Rodwell joined from Everton earlier this month and back-up goalkeeper Richard Wright arrived on Thursday.
The trio could be joined by Maicon, Javi Garcia and Matija Nastasic as City look to further strengthen their squad on the final day of the transfer window.