The 21-year-old centre-half joins NAC on a season-long loan. He spent part of last season on-loan in Belgium with KV Kortrijk.
NAC chief Hans Smulders stated: "Before we went into the summer break we looked at positions that have to be filled for the new season. On that basis we looked for players.
"The wings have been filled in and with Erik we now have the desired reinforcement for the central defence. Erik is a player with speed and he is also strong in the one-on-one duels. He naturally has a drive forward and thanks to his good passes he can be an important link in the build-up."
Palmer-Brown also said: "I watched many Eredivisie matches last season. The style of play is good to me. I also heard a lot of good things about NAC. I've heard from players from the Eredivisie and I know that the supporters' support is incredible."