The striker has joined Luke Coulson and JJ Hooper in joining the National League club.
Hines is back nearer home after Chesterfield manager Martin Allen allowed him to leave to return to London.
Bromley boss Neil Smith is happy with his work over the past few days, saying: “It’s been a very busy week on all fronts.
“It’s a fantastic bit of business for the Club and there’s been a lot of hard work behind the scenes to get these deals done.
“Zavon is a top quality player with the experience we need, and did very well playing against us last week.”
Bromley face a National League trio to Gateshead on Saturday.