Alexander, who became chief executive in 1997, will step down at the group's AGM on 15 July. Andrew Rashbass, the publisher and managing director of The Economist, will replace her.
Alexander joined The Economist in 1985 as its marketing manager and became managing director of the Economist Intelligence Unit, the business information arm of The Economist Group, before taking her current role.
She will continue to work as a non-executive director of Centrica and Rolls-Royce.
Alexander said: "I'm proud of what we've achieved, and privileged to have led such a winning team. It's the right time for me to move on."
Sir Robert Wilson, the chairman of The Economist Group, said: "She has been a hugely successful chief executive and leaves a marvellous business legacy, including a dynamic successor."
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