Mr Irvine is to give up all executive duties at Reed Elsevier on 2 July when he becomes 60. But he will continue as chairman of Reed International until the annual general meeting next April.
Mr Stapleton, who becomes co-chairman of Reed Elsevier and of its executive committee alongside Herman Bruggink on 2 July, will continue as deputy chairman of Reed International until next April, when he will become chairman of the company.
Mr Irvine, who became co-chairman of Reed Elsevier following Peter Davis's acrimonious departure in 1994, said: "I have enjoyed my two years as co-chairman of Reed Elsevier, during which time the business has made excellent progress."
Mr Stapleton, 49, whose wife is Dutch, has been chief financial officer since the formation of Reed Elsevier in January 1993, and has been finance director of Reed International since 1986.
He is also a non-executive director of Allied Domecq and a member of the Financial Reporting Review Panel, the financial accounts watchdog that works alongside the Accounting Standards Board. From 1994 to 1995, he was chairman of the 100 Group of UK Finance Directors and prior to joining Reed in 1986 held various management positions with Unilever.
Mark Armour, deputy chief financial officer of Reed Elsevier, will succeed Mr Stapleton as chief financial officer of Reed Elsevier and finance director of Reed International.
The arrival of Mr Armour from accountants Price Waterhouse last year has enabled him to take on greater operational responsibilities in recent months.
Mr Armour, 41, was an adviser during the merger of Reed and Elsevier and then led the PW team auditing and carrying out other accounting services for the company.
Mr Irvine, previously deputy chairman, oversaw a period of consolidation at Reed Elsevier following Mr Davis's abrupt resignation. Mr Davis, now chairman of Prudential, the insurance group, was to have become sole chairman of the combined group but stepped down over a clash over his role with fellow members of the company's executive committee. He later received more than pounds 1m in compensation.
Last year, Mr Irvine's pay rose from pounds 630,700 to pounds 725,700, including a pounds 225,700 performance-related bonus.