He signed from Serie A side Inter Milan for an undisclosed fee.
"Roberto Mancini is an admirer of the 31-year-old having worked with him for two seasons while in charge at Inter and the defender is familiar with the 3-5-2 formation the City boss has been experimenting with in pre-season," the club said on their official website.
Maicon played 235 matches for Inter, scoring 20 goals, and will link up with his new team-mates when he returns from international duty next week.
Sinclair also arrived for an undisclosed fee from Premier League rivals Swansea.
The 23-year-old winger was a member of the Britain team at the London Olympics.
"I'm just glad everything is settled and that I'm now a City player," Sinclair told the 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."
Sinclair could be included in the City squad for Saturday's home game against Queens Park Rangers.
Wright joins the club as third-string goalkeeper behind Joe Hart and Costel Pantilimon.
He was a free agent after leaving League One club Preston North End.
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