Telfer, 20, cost United £200,000 when he joined from Rangers at the beginning of last season.
However, he has made only eight appearances this season, the most recent of which was in December.
Last term, Telfer netted four times for the Tangerines and he could make his Livi debut away to Dumbarton on Saturday.
The West Lothian side are currently second bottom of the Championship while United are bottom of the Premiership.
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Dundee United midfielder Charlie Telfer has joined Livingston on loan for the rest of the season.