Villa have taken on the former Swansea player with a view to signing him permanently in the summer.
Sinclair said: "It's taken a few weeks but I'm happy to be here, to be in the building and to be signing for the club and ready to play some football.
The 25-year-old has made just 19 appearances for City since joining them back in 2012, with an unsuccessful loan stint at West Brom last season.
"It's nice to be able to get settled somewhere and be a part of something going forward," he added.
"It feels great to be here and that the deal is finally done.
"I spoke to the manager (Paul Lambert) and he gave me his views on what he wants from me here at Villa.
"I'm still hungry to play football, that's what I told him, and I'm looking forwarding to getting started, hopefully playing every week and enjoying my football."
Source : PA