The switch to the Baggies is the 24-year-old's seventh loan move in six years, but he feels happy at his new club and wants to get going.
The former Swansea winger moved to City last year for around £6million, but only played 11 league games for the then-champions, forcing him to consider other options.
Talking to the Express & Star, Sinclair said: "I only had three starts in the whole season. But I'm so happy I'm here and I'm looking forward to the season, getting games in and hopefully scoring goals.
"It was a very frustrating season, being at City and not having the chance to play.
"Hopefully now I can get back on track and get my career going again and just be happy to be playing."
Sinclair is likely to be involved at Everton on Saturday and West Brom boss Steve Clarke is looking forward to seeing his new signing in action.
Clarke said: "He had a couple of great seasons at Swansea, got the big-money move to Manchester City and he feels he didn't get the chances there he deserved to play in their team, and I think he is probably right on that.
"He comes here hungry and determined to prove he is still the quality player he showed he was at Swansea. He is desperate to play this weekend.
"He is looking for a nice quiet house out in the country here - he said he doesn't want to stay in the town centre, which is music to my ears!
"He is looking forward to living somewhere nice and quiet, and just concentrating on his football. I think it is a big year for him."