More than 20 schools were told to stay closed on Monday in response to the threat posted on internet forum 4chan. The suspect is a former pupil of the British School, which has a site in neighbouring Voorschoten, a municipality close to The Hague and to Wassenaar, the residence of the future kings of Netherlands.
The anonymous writer said they would shoot their teacher "and as many students as I can".
The threat was picked up by Swiss police during internet checks at the weekend, Dutch media report.
The school said the suspect left its senior school in October 2011 as a result of inappropriate behaviour.
Earlier Leiden Mayor Henri Lenferink said the decision to close the schools had been taken because police had not been able to immediately establish the perpetrators of the threat following the tip-off from Zurich.
Head teachers had a meeting in order to agree if schools shall be closed on Tuesday.