The former Feyenoord man has agreed a 93-day loan deal with the Terriers, and completed the paperwork at the American Express Community Stadium this afternoon.
He will travel to Huddersfield this evening and would be available for his debut in their match at Preston North End this Saturday.
Manager Chris Hughton commented, "Elvis is keen to play regular football, and we are not able to guarantee him that here at the moment.
"At Huddersfield he will have the opportunity to play more regular football in the Championship, which will be to everyone's benefit.
"It's also ideal for us that he is remaining in England, and in particular the Championship, as that means we can monitor his progress."
Having played for both Albion and Feyenoord this season, Manu is not able to sign for a third club on a window-to-window loan, which means he is restricted to joining Huddersfield on an emergency loan.
Manu joined Albion last August, but found his opportunities restricted during the first half of the season, with the team in such fine form and Hughton able to name a settled side.
He has been limited to just eight sub appearances for Albion, with his solitary start coming in January's FA Cup third round tie at Hull City.