The Ravens talented attacker joined the League One club for a club record undisclosed fee on Tuesday.
Pompey have a rich recent history in signing National League players, with Jamal Lowe joining with great success from Hampton & RB, as did Oliver Hawkins who left Dagenham to play for the former Premier League club.
Bromley have moved quickly to enhance their squad with towering defender Michael Chambers joining from Wrexham.
A club statement on Hackett-Fairchild read: “Despite losing a prized asset, the club are extremely proud to add Reeco to the number of players who have represented the club with such professionalism, developing under the guidance of the club and Neil Smith.
“Whether it be players on loan, or our own, Reeco joins a number of players such as Louis Dennis, Luke Woolfenden, Brandon Hanlan, Rarmani Edmonds-Green and Alfie Doughty, who have all gone on to play in the Football League following spells with the Ravens.
“This further enhances the reputation of the club in the professional footballing world, which is something we take great pride in.”
New man Chambers said: “You can see the club’s ambition and I’m excited to be a part of it.”