Mr Stapleton will receive pounds 140,000 and Mr Bruggink will be paid 500,000 Dutch guilders - on top of their normal pay packages - as compensation for staying with the company until May while it tries to find a new chief executive.
The payments were prompted by Reed Elsevier's decision last August to move to a unitary board with a single chairman and a single chief executive.
Until now, Reed has been run by a four-man executive committee with Reed International and Elsevier, the English and Dutch holding companies, each supplying two members. At the time both Mr Bruggink and Mr Stapleton indicated they would not be candidates for the post.
The shake-up is believed to have been caused by a boardroom rift after the collapse of Reed Elsevier's proposed mega-merger with its Dutch rival Wolters Kluwer last summer.
According to Reed Elsevier's annual review, which was sent to shareholders this week, the shake-up gave Mr Bruggink and Mr Stapleton "the right to treat their employment with Reed Elsevier plc as having been terminated immediately". However, both men agreed to stay on until May.
Reed Elsevier has yet to formally appoint a new chief executive, although it is expected to announce the appointment before its AGM. Jonathan Newcombe, chairman and chief executive of US publishing house Simon & Schuster, is believed to be a leading contender. Morris Tabaksblat, the former chairman of Unilever, has been lined up to take over as chairman.
A spokeswoman for Reed said the company was paying the bonuses to Mr Bruggink and Mr Stapleton "in recognition of their commitment to the company". She refused to say whether they would also be receiving compensation for loss of office when they eventually left.
Mr Stapleton saw the total value of his pay package rise 29 per cent to pounds 707,000 last year while Mr Bruggink was paid Dfl1.63m, up 10 per cent. This was despite Reed's adjusted pre-tax profits falling 6 per cent to pounds 773m during the year.
Meanwhile, Robert Wilson, chairman of Rio Tinto, the mining giant, was paid a total of pounds 848,000 - an increase of 27 per cent - in 1998 even though Rio Tinto's adjusted earnings dropped 10 per cent.Reuse content