BAe confirmed last night that Mr Cahill, who became executive chairman in May 1992 on a five-year contract, will leave after the next annual meeting.
He is to receive compensation of dollars 4.7m ( pounds 3.3m) - the value of his share options - but will not be paid compensation for his contract. There had been speculation that Mr Cahill, whose salary was dollars 800,000 a year, would receive a pay-off of several million pounds in addition to his share options.
Mr Bauman, who retires from SmithKline Beecham in April, will be non-executive chairman on a salary of pounds 50,000. He will also take 120,000 share options exercisable at 550p.
The boardroom change was announced too late to affect the British Aerospace share price, which closed down 6p at 543p.
BAe's articles of association will have to be changed to make way for the appointment of Mr Bauman, who is a US citizen although he lives in the UK. The new chairman is also a director of Capital Cities/ABC, Union Pacific, Cigna Corporation and Reuters Holdings.
Mr Cahill's reputation had suffered because of BAe's abortive attempts to put its loss-making regional jets business into a joint venture with Taiwan Aerospace Corporation. In 1990, he retired early as chief executive of BTR after the group failed to acquire the US Norton abrasives group.
The BAe spokesman said that Mr Cahill had made an important contribution in changing the culture of the defence business towards being more competitive and cost-effective. 'He has achieved the majority of tasks agreed when he joined and as a consequence the role of chairman has changed,' he said.
BAe added that substantial progress had been made during Mr Cahill's term in restoring the group's financial position and refocusing on core activities, culminating in the agreement earlier this month to sell the Rover automotive group to BMW for pounds 800m.