Mr Van Gelder spent less than six months in the post, but decided to leave over the weekend, following Friday's appointment of David Hilton in the new post of chief executive.
Mr Hilton was occupying Mr Van Gelder's office yesterday, and calls to Mr Van Gelder were directed to a mobile telephone number which he did not answer. Mr Van Gelder, 43, was formerly managing director of Teletext before joining BIB in June.
A spokesman for BIB said: "Mr Van Gelder has decided he isn't going to stay on as managing director. He will continue to work with BIB to effect a smooth handover, but he has decided on reflection he'd be better off pursuing interests elsewhere." The spokesman would not comment on Mr Van Gelder's compensation package, nor on his current salary.
BIB, which is to provide interactive services for digital television, is to make further senior appointments shortly in an attempt to boost its management team. Sources close to the company said the boardroom shake- up came at a sensitive time. The European Commission recently sent BIB a list of concerns focusing on the link-up of dominant players such as BT and BSkyB.