Ferguson left Port Vale by mutual consent in January, having made just one appearance for the club.
The 21-year-old had a loan spell with National League side Southport earlier this season, featuring in six games.
Former Chelsea trainee Omofe, 19, signed a short-term deal with Bristol City in June 2016, but did not make a first-team appearance for the club.
Bromley have signed former Port Vale midfielder Nathan Ferguson and ex-Bristol City player Shabazz Omofe.