The 26-year-old midfielder has already spent more than three months at Villa Park, having joined on loan in January. He has penned a four-year deal with the Premier League club.
Sinclair has made 11 appearances since moving to Villa, including three in the FA Cup.
The Bath-born player told Villa’s official website: “We’ve had a fantastic end to the current season – and now I am already looking forward to the new one.
“It was important for the family to have that stability and I’m thrilled it’s with a club like Villa.
“This is the happiest I have been in a long time. Now it’s about kicking on with my career in claret and blue.
“I have already loved every minute of playing for this club. To be a permanent Villa player now is a fantastic feeling.”
He has scored three goals for the FA Cup finalists and has just recovered from injury, adding: “My aim now in the closing two weeks is giving 100 per-cent in training and waiting for my next chance.”