Latics boss Roberto Martinez has spoken openly of his hope of landing Britton on a Bosman in the coming weeks.
But the 27-year-old, who joined the Swans back in 2003, turned down offers from Premier League clubs in favour of a move to Bramall Lane and has agreed a three-year deal with the option of a further year.
He told the club's official website: "There was interest from the Premiership and I spoke to a couple of people there but it wasn't right for me - Sheffield United was.
"First and foremost this is a massive club, you only have to look at the average attendance last season. I was here with Swansea for the penultimate game and the special atmosphere from that day is still fresh in my mind."
United manager Kevin Blackwell added: "It has been a protracted process because it started after we played Sheffield Wednesday in mid-April when we had arranged to meet in the hotel and I began preliminary talks with him.
"Leon is a player of real quality, the sort we have missed at this club since the days when we had Stuart McCall and Michael Brown in the middle of the park."