Striker Osborn left the club at the end of last season but has since been invited back by manager Wayne Burnett before penning a one-year deal.
The former Grays forward will now join non-league outfit Ebbslfeet on a season-long loan deal.
Goldberg has also agreed a one-year deal after leaving Hastings and will link up with father Mark, who is manager of Bromley on a season-long loan also.
"I am delighted to have signed both boys," Burnett told the club's official website. "Alex has worked extremely hard in his time here.
"Bradley is also a player who has caught our eye during pre-season. Both will now spend time out on loan to gain first team experience."
- Sports & Recreation
- Wayne Burnett