Lichaj, who could go straight into the United squad for Saturday's game at Bristol City subject to the formalities of the deal being completed, previously spent loan spells at Lincoln and Leyton Orient.
Simon Grayson told the club's official website: "A deal has been agreed for Eric to join us and we're delighted Aston Villa have agreed to let him come. He is a player that they have high hopes for and they believe him coming to Leeds will be beneficial for him and us.
"A few other Championship clubs were interested so we are delighted to get a player that has played international football at different levels."
Source: PA