The 30-year-old joined in November and has been credited by manager Neil Warnock as having been key to United's recent improvement.
Tate played in Tuesday's 1-0 win over Bolton - Leeds' fifth straight home league win - and will now remain at Elland Road until January 27 at least.
West Brom winger Jerome Thomas, who joined on the same day as Tate, has returned to The Hawthorns, with Warnock saying he believes other clubs are interested in the former Arsenal man.
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- Neil Warnock