The out-of-contract Swansea midfielder, 27, was expected to join his former boss Martinez at Wigan but they failed to come up with the deal he wanted.
Middlesbrough were also interested but Britton signed for United on Friday on a three year contract that doubled his wages.
Blades runner: Free agent Leon Britton opted against a move to Wigan to join Sheffield United instead
Britton said: 'There was interest from the Premier League and I spoke to a top-flight club, but decided that coming to United was the right move for me. United are a massive club with really big ambitions and I believe I can help them make a push for the top flight next season.'
Manager Kevin Blackwell has already signed striker Daniel Bogdanovic and defender Johannes Ertl on frees from Barnsley and Crystal Palace.
He now hopes to complete the £750,000 capture of Stoke keeper, Steve Simonsen, 31, within the next 48 hours.
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Source: Daily Mail
Source: Daily Mail