The Londoner signed for the Blades in the summer under Kevin Blackwell, but Leon was quick to admit himself that things haven't gone as smoothly as hoped.
The club has confirmed that Britton joins the Swans for an 'undisclosed fee', but that is more likely to mean fees for appearances made etc.
Britton hadn't settled to life at Bramall Lane, but having three permanent managers and one caretaker manager in his brief stint at S2 did him no help.
On leaving the Blades, he said: "I am gutted that things haven't quite worked out the way we all hoped but I am grateful that United showed faith in me in the first place. Despite being there only a few months I made a lot of friends at the club and I would like to thank the fans who were always supportive of me."
On Swansea City's official website Leon admits he wished he had never left the Liberty Stadium, but said he liked what he heard from then Blades manager Kevin Blackwell.
Micky Adams commented: "Leon is a good player but sometimes moves just don't come off and it isn't anyone's fault. He had established his life in Swansea and his girlfriend still lives there. They have found things quite difficult and we have to respect his private life so we all just have to move on.
"My sole aim is to get this club up the league and when one player goes it means another has an opportunity. I can't afford to get sentimental about who is in and who is out because my job is to just win football matches, but Leon is a good lad and I wish him all the best."
Finally, Chief Executive Trevor Birch said: "It is extremely disappointing to lose Leon but he wanted to go back to Swansea because of his personal circumstances which weren't conducive to him being able to settle fully up here.
"Although he has great qualities and we understand his reasons, in the situation we are in we need players who are committed to the cause and want to play for Sheffield United. We are fortunate to have Lee Williamson back in contention and will use this opportunity to continue our search to strengthen the squad."
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