The striker - who scored 28 goals for Falkirk before moving south in July 2012 - will be available to play once United receive international clearance.
The 28-year-old was also a target for Partick Thistle this month, with the Firhill club instead bringing in another former Falkirk striker, Lyle Taylor. The arrival of El Alagui coincides with David Goodwillie's return to parent club Blackburn Rovers following a short-term loan at Tannadice
"This is the ideal time for us to bring in Farid," said Jackie McNamara, the United manager. "He will bring something a little different from what we have at the club and will enhance our attacking threat."