The 21-year old could not make an impact at White Hart Lane so has agreed to a six-month deal with the Bundesliga side with the option of a permanent move included in the short-term deal.
Borussia coach Michael Zorc confirmed the move on the club’s official website.
“We have taken him on a six-month loan until the end of the season,” he said.
“We expect his arrival tonight (Sunday) in Malaga, and he will practice with the team for the first time on Monday.
“We want to watch him first (before taking a decision regarding a permanent move) because he has been going through a difficult period.”