The 24-year-old struggled for playing time at the Etihad Stadium after joining City from Swansea last summer.
He played in only 11 Premier League games under Roberto Mancini last season and was not involved on the opening day of 2013-14.
Sinclair is also well known to Albion boss Steve Clarke, who watched his progress through the ranks at Chelsea.
"Scott understands he needs to play football and it will be good to work with him again," Clarke told the club's official website.
"We're delighted he feels this is the right club for him at this stage of his career. He is the type of player we were missing from the squad.
"He is a pure winger, who is quick, direct and scores goals - he has proven that over his career. He can play off the right or left and improves our attacking options.
"I know him well and he is a good person, who I know is 100 per cent committed to our cause.
"He is frustrated he did not get the chances to play at Man City last season and hopefully he will take those frustrations out on Premier League defenders this season."