King, who has worked in the defence industry for 40 years, has led the group since September 2008.
"After a distinguished career, Ian will retire leaving a legacy of disciplined performance, ethical behaviour, a burgeoning order book, a track record of delivering shareholder value and a strong leadership team," said chairman Roger Carr.
"Ian has built a world-class defence engineering and technology business, providing vital capabilities to our customers and contributing to the security and economic prosperity of the nations in which we operate," he added.
His successor Woodburn spent 20 years in the oil and gas industry, notably at Franco-American group Schlumberger, before joining BAE in May 2016.
Woodburn's promotion was widely forecast by analysts ever since he joined the group in the newly-created role of chief operating officer.
Howard Wheeldon, an analyst with Wheeldon Strategic Advisory, said the announcement "will be welcomed throughout the company, by investors and by all those that the company serves.
"Apart from energy, enthusiasm and very experienced approach, Charles Woodburn brings over 20 years' international experience, primarily from the international oil and gas industries, gained in a number of senior management positions," he added.
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