The 22-year-old United States international made his Villa debut in August and has since gone on to make a further seven appearances, including five in the Barclays Premier League.
Lichaj previously spent loan spells at Lincoln and Leyton Orient.
Whites boss 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."