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Sinclair was part of a Villa side that was relegated from the Premier League last season, having joined the club permanently in 2015 following a loan spell from Manchester City.

The 27-year-old will now try to rejuvenate his career with the Scottish Premiership champions and he is reunited with new Celtic manager Brendan Rodgers, who he played under at Swansea City.

Sinclair got off to the perfect start for his new club, coming off the bench to score the winner in the 2-1 win over Hearts on Sunday (AEST).

"It feels amazing to have joined Celtic," Sinclair, who cost a reported $6 million, said in a statement on the club's official website.

"I had to look at this move and I thought it would be great for me. And because I know the manager and I know what to expect, hopefully I can get off to a flying start.

"The manager had a great influence when I was at Swansea and that's when I played my best football. Hopefully now I can get the best football out of me and get my form back out there and score goals and perform."

Once considered among the brightest prospects in English football, Sinclair failed to break into the first team on a regular basis at Chelsea before impressing at the Liberty Stadium.

His form for Swansea from 2010 to 2012 earned him a move to City, where his career again stagnated.

A member of the Great Britain team at the London Olympics in 2012 but never capped at senior level by England, he hopes to get a taste of elite European football, should Celtic overcome Hapoel Be'er Sheva of Israel over two legs of its Champions League qualifying play-off. 

"I watched the Astana game in midweek and the atmosphere was incredible," he said, referring to a 2-1 home win in the second leg of the third qualifying round against Kazakh opposition. 

"To have the possibility of Champions League football excites me and I can't wait to come here and play at Celtic Park and for it to be rocking."