The agency has been without a management-level planner since the departure of Russ Lidstone to JWT London in the spring of 2005.
In her new role, Morgan will be charged with developing broader strategic thinking at the agency.
She will take up her new position in July 2006 and will sit alongside the Lowe management team, which includes the executive creative director, Ed Morris, the managing director, Chris Hunton, and the chief marketing officer, Judy Mitchem.
The appointment comes as a question-mark hangs over the management structure of Lowe's London office. Garry Lace, the agency's chief executive, is currently suspended pending an investigation by Lowe's Interpublic parent.
Morgan joined BT in September 2004 after spending 11 years at Bartle Bogle Hegarty, where she was the head of account management and, latterly, the BBH group planning director.
Tony Wright, the chairman of Lowe, said: "Morgan is not just a planner - she falls into the category of grand strategist. In my view, Morgan and Morris will be the best planner-and-creative duo in London."
Morgan said: "At heart, I am a strategist. This role represents an opportunity to shape the business, bringing to bear the breadth of my experience from BT and my first-hand business and marketing knowledge. In the future, the importance of strategic and communications ideas will increase - Lowe can only thrive in that environment."