The 6-foot-6 Gee played in 11 games with the Wizards last season, when he signed two 10-day contracts before leaving to join the San Antonio Spurs.
He appeared in five games with the Spurs this season, scoring a total of two points, before being waived last week.
Hudson shot 0-for-9 in his six games with Washington this season.
The Wizards are 4-8 and in last place in the Southeast Division. They host the Philadelphia 76ers on Tuesday.