The 20-year-old youth international, who impressed Feyenoord in a trial earlier in the year, passed a medical on Tuesday prior to signing a one-year contract with the Kuip club.
Brosque, who has a two-year option in place, will not be at De Kuip for long as he has agreed to take an immediate loan move to Feyenoord's Belgian partner club Westerlo.
"I think it's good," Brosque told Feyenoord's website of his move. "Your first year away from home is always tough and it's important that you play, in the first team and not in the youth team. I can do that at Westerlo.
"What's more, in Jan Ceulemans the club also has a trainer I can learn a great deal from. I hope to be good enough to return to Rotterdam. Feyenoord is my goal."
Another player tipped to head out of Feyenoord on loan is Ferne Snoyl, with Twente expected to seal the 19-year-old's signature later in the week.
