Ellis was suspended for the first game of the season and fined $100,000 by the NFL for violating the league's substance-abuse policy last season.
Ellis was arrested last November and charged with possession of marijuana, speeding and driving without insurance after being pulled over by police in Hanover, N.J., a few miles from the team's training facility in Florham Park.
He's expected to play in the Jets' home opener against New England on Sunday.
Cole, signed as a free agent in February, was inactive for the Jets' 24-7 win at Houston on Sunday.
Copyright 2009 by The Associated Press