The breakaway body launched in April after a long breakdown in relations between the Russian-led International Boxing Association (IBA) and Olympic organisers.
The International Olympic Committee (IOC) stripped the IBA of recognition last June, after years of suspension, due to its failure to complete reforms on governance, finance and ethical issues.
World Boxing said Van der Vorst secured 63% of the vote against Elise Seignolle of USA Boxing and will serve an initial two-year term.
The body's inaugural congress in Frankfurt was attended by 26 of World Boxing's 27 member countries.
Van der Vorst told reporters in a video call that it was the start of a new era and he expected more members to join once the Swiss-based Court of Arbitration for Sport (CAS) had ruled on an IBA appeal against the IOC.
"We have set a foundation for our new international federation," he said.
"In the last weeks, several national federations contacted us but were after the deadline and couldn't take part in the congress. We are pretty confident that many will follow.
"We think that after the CAS decision with the IOC and IBA the membership will accelerate... we know that there are several national federations on the fence waiting for the CAS outcome."
Van der Vorst would not set a timetable for IOC recognition, saying expanding the membership and organising successful competitions were the immediate priorities.
Boxing is expected to be part of the 2028 Los Angeles Games after being left out of the initial programme.
"I am optimistic," said Van der Vorst.
"We will work hard. We won't give up. We have maybe received eight counts several times but I feel really there's a chance for one of the remarkable comeback stories in the Olympic movement and that's what we're going to do."
Van der Vorst stood last year against Russian incumbent Umar Kremlev for the presidency of IBA but was controversially deemed ineligible to stand two days before the vote, with Kremlev then elected unopposed.
The CAS later ruled that the Dutchman had been wrongly prevented but an extraordinary IBA congress in Armenia last September voted not to hold a fresh election.
