Keeper Zoetebier has been allowed to move on by Feyenoord coach Ruud Gullit, while Belgian international midfielder Goor joins from Hertha Berlin.
Goor has signed a two-year deal and the club feel he could become a cornerstone of their team.
"Bart is an experienced left-footed midfielder who we can really use in Ruud Gullit's system," Kuip technical director Mark Wotte told the club's website.
"We see him as one of the future foundations of the team."
Zoetebier has been deemed surplus to requirements by Gullit and he had no objection to him joining Feyenoord.
Gullit has Gabor Babos and Patrick Lodewijks battling it out for the first team jersey, which would have left Zoetebier with little hope of action.
PSV coach Guus Hiddink has been seeking an experienced custodian to replace the departing Ronald Waterreus and he has now settled on 34-year-old Zoetebier.
