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.
He impressed for the Welsh club’s U21 team last season, scoring 18 goals and providing 10 assists.