Hackney-born Omozusi played eight Premier League games for Fulham prior to his release from Craven Cottage this summer.
O's boss Russell Slade told the club's official website: "Elliot is a young defender who comes here with a good pedigree having played in the Premier League with Fulham and on loan with Norwich and Charlton.
"He is a good athlete, he likes to get forward and he passes the ball well. He is also strong in one-against-one situations and we had the opportunity to view him last season when he trained with us for a couple of weeks.
"By his own admission he wants to get his career back on track and it's a good opportunity for both him and the club to move forward."