The 30-year-old centre-half, who first arrived on loan at Elland Road at the end of November before both clubs agreed to extend his stay for another month, has made a total of 11 appearances for Leeds.
"We can't thank Alan enough for his help over the past month and thanks also to Swansea for allowing him to come here," Leeds manager Neil Warnock told the club's official website. "He has returned to Swansea now and we wish him all the best."
Tate made his debut for Leeds in their home win over then npower Championship leaders Crystal Palace on November 24 and started in all of his other appearances for Warnock's side, playing his last game in the recent defeat at Barnsley.
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