The midfielder is a surprise departure from Bramall Lane considering he has been a first-team regular for the Blades since arriving in the summer, penning a new two-and-a-half year deal at the Liberty Stadium for an undisclosed fee.
Britton, out of contract at the time, swapped Swansea for Sheffield having rejected a new deal in search of a change of scenery, bringing an end to an eight-year spell in which the fans' favourite wracked up almost 350 appearances.
But the move has not worked out with Britton failing to settle in Yorkshire with his girlfriend still living in south Wales, and United struggling at the wrong end of the Championship, with the 28-year-old having worked under four different managers just 26 games into a three-year contract.
Those factors combined with Brendan Rodgers' strong desire to work with Britton - who left Swansea when Paulo Sousa was still in charge - has paved the way for the deal, with current Blades incumbent Micky Adams looking to utilise the freed up funds for new recruits of his own.
Britton told Swansea`s official website: "It was a mistake and I should never have left Swansea. Hindsight is a wonderful thing and none of us would make any mistakes if we knew what was ahead of us."