Gorre signed a new three-year contract at the Liberty Stadium on Monday after making his senior debut at Crystal Palace on the final day of last season.
The 20-year-old will now return to his native Netherlands to gain further first-team experience at the Eredivisie club.
“I was delighted to sign the new deal and the loan move to Den Haag is a bonus,” Gorre told the official Swansea website.
“It’s a good club that plays its football at a high standard.”
Gorre, the son of former Ajax and Feyenoord midfielder Dean, joined Swansea from Manchester United in 2013.