The 6ft 2in defender, who also had a trial at Sheffield United, will bolster Gary McAllister's ailing back four.
He has experience of playing in France with Montpellier and Germany, and as a free agent, Leeds have been able to sign him outside the transfer window.
Assoumani was born in Nice and has played for Montpellier and German clubs FC Saarbrucken and Sportfeunde Siegen.
International clearance has been secured and he is available for selection for Saturday's fixture with promotion rivals MK Dons.
The defender played and scored in last night's reserve-team meeting with York City at Elland Road, with United winning 3-1.
"He's looked good in training and settled in well," said McAllister. "He instantly comes into the reckoning for Saturday's game."