The signing, which will surely be seen as a big coup for the Swans, is Brendan Rodgers' first since arriving at the Liberty Stadium.
Sinclair spent last season on loan at Wigan and scored twice for Roberto Martinez's men, who had declared an interest in retaining the services of the pacey wideman on a permanent basis.
The 21 year old played 14 times for Chelsea, scoring once in a cup tie, and has also spent time out on loan at QPR, Birmingham and Crystal Palace.
Swansea will pay an initial £500k fee, with the deal rising to a possible £1m with performance related add-ons.
"Scott is obviously a player I know well and I am delighted to sign him,'' explained boss Brendan Rodgers.
"It's a massive coup for us because he is a big talent and has been a sought after player since he broke on to the scene.
"As far as I am concerned, there's no better place for him than Swansea City. With this group of players, style of football, fantastic fans and a manager who knows him well, this will be a great club for his development.
"He is only 21 and still has big potential. I think this will be a good home for him, where he can come and play and realise that full potential because I know what he is capable of.
"He is a great signing for the present and the future and joins a group of exciting young players that includes the likes of Joe Allen, David Cotterill and Nathan Dyer."
Swans chairman Huw Jenkins said: "While everyone is aware that we run a tight ship here financially, we will always invest in the team when funds are available. I think this signing highlights our intent.
"It is also the club's priority to invest in bright, young talent wherever possible – and I don't think you will find many young players with the talent that Scott possesses.
"We have been fortunate that he has worked closely with Brendan in the past. Brendan was one of the attractions for Scott, but there was also the style of football we play and the fantastic playing surface we have here at the Liberty Stadium.
"I'm sure our supporters will be excited about Scott joining us and watching him perform in a Swans shirt.''
Welcome to Swansea, Scott.
This article first appeared on JACKARMY.net.