The 30-year-old centre-half was due to return to Swansea after the New Year's Day win over Bolton, but will stay on at United until the Middlesbrough game at the end of the month.
Tate, who has made nine appearances since arriving at Leeds at the end of November, has been given permission to play in the FA Cup and is expected to feature in the third-round clash with Birmingham on Saturday.
But winger Jerome Thomas has returned to his parent club West Brom following the end of his loan spell.
The 29-year-old was also scheduled to return after the Bolton game, but returned to the Hawthorns early due to illness.
Neil Warnock has confirmed his interest in keeping hold of Thomas, who will discuss his future with West Brom, while talks are ongoing between the West Yorkshire club and Stoke over the future of midfielder Michael Tonge.