The 25-year-old left the SPFL Championship club to sign a three-year contract with United in the summer of 2012 but returned on loan in October having failed to make an impact.
He has played an integral part in Falkirk's seven-match unbeaten run, though, scoring twice during that spell. That convinced Falkirk to request that his stay be extended - Millar had been due back at United this month - as the club continue to entertain hopes of challenging for promotion this season.
Falkirk are seven points behind leaders Dundee, with the Dens Park side last night considering offering a contract to former Hearts striker Christian Nade. The Frenchman has been training with the club.