The pair will now team up with fellow countryman Ahmed Elmohamady, who has returned for a second spell on loan from Sunderland until the end of the season.
Both Nagy and Fathi signed their deals ahead of Thursday's transfer deadline, but will not join up with Steve Bruce's squad until next week.
Striker Nagy, otherwise known as Gedo, has scored 17 goals in 32 appearances for Egypt and starred in their triumphant African Nations Cup-winning side in 2010, in which he won the golden boot.
Fathi, a versatile right-sided player, has had a previous spell in England with Sheffield United in 2007 and is also an experienced international.
The pair will be joining up with compatriot Elmohamady, who has returned to the KC Stadium on loan until May.
The wing-back made 25 appearances for the Tigers earlier this season during an initial stint on loan from Sunderland.