Green joined BT in 1986 and is currently CEO of group strategy and operations. He will take up his new role on 1 January 2008.
Green was central in rolling out BT's broadband business and led BT Global Services from 2001 until this April.
Green said, "I am excited by the new challenge that becoming the CEO of LogicaCMG provides, and delighted that I will continue to have the opportunity to work with BT as a business partner."
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Green will stand down from the BT board in the near future, said BT.