El Alagui, who plays for English League One side Brentford, is set to replace David Goodwillie in the Dundee United attack. Goodwillie is due to return to parent club Blackburn Rovers next week.
Manager Jackie McNamara hailed the signing of El Alagui, who scored 18 goals in his last spell in Scottish football in 2012.
He said: “This is the ideal time for us to bring in Farid. He scores goals, has strong aerial ability and will hold the ball up and allow his fellow attackers to get involved.
“We have moved quickly to secure him because there was interest from other clubs and I am delighted to sign him. He will bring something a little different from what we have at the club and will enhance our attacking threat.”