The USA defender has been filling in at right-back for the injured Paul Connolly and will now see out the campaign at Elland Road.
"Eric has done well since he came here," Simon Grayson told the club's official website. "He's showed his qualities and he gives us good competition in the right-back area.
"We're delighted Villa have agreed to allow him to remain here until the end of the league season."
The 22-year-old was joined at Leeds last week by Villa team-mate Barry Bannan, who signed on loan for the rest of the season.