Goal.com exclusively revealed on August 8 that the Premier League champions have agreed terms with the Team GB star after deciding to let winger Adam Johnson go and Swans boss Michael Laudrup confirmed on Friday that the attacker had decided not to sign a new contract.
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"He's been terrific for us, to be fair - we've had two seasons out of him and he was superb in the Championship and virtually his goals [27 in 2010-11] got us promotion.
"And last year as well he wasn't maybe quite as effective as he was his first year - obviously it was a lot tougher opposition - but he's been absolutely magnificent.
"Like Joe [Allen, now of Liverpool] we wish him all the best, but as long as the club keeps pushing forward that's the main thing.
"It obviously gives Scott the chance to settle in at his new club and it gives us the opportunity to buy a replacement for Scott."
Sinclair scored the last of Swansea's goals in their 5-0 obliteration of QPR on the Premier League's opening day.