The club parted ways with Priske on Monday, citing inconsistent results and a lack of chemistry as the main reasons, with Feyenoord fifth in the Eredivisie standings and 12 points behind leaders Ajax Amsterdam.
Bosschaart spent two seasons as a player at Feyenoord between 2004-2006 and has been in charge of the Under-21 team at the club after assistant coach spells with SC Cambuur and FC Dordrecht.
"We are pleased that Pascal has immediately shown his willingness to step in temporarily," Dennis te Kloese, technical director of Feyenoord, said in a statement.
"In the meantime, I have been able to speak to many players, staff members and other people closely involved and everyone realizes that we still have a lot to fight for."
Feyenoord host Milan in the first leg of the Champions League knockout phase playoff on Wednesday.
