HP has hired Mackenzie, who has overall control of BT's £100m advertising budget, as vice-president of marketing for the EMEA region.
Mackenzie, who takes up the role in mid-August, will report to HP EMEA chief executive Kaspar Rorsted.
She will be responsible for stepping up the fight against IBM and Microsoft by overseeing new product development. She will also chair HP's marketing council, which coordinates European marketing activity.
It is unclear who will replace Mackenzie at BT and sources have suggested that her exit could force a major shake-up of the company's marketing department.
BT business marketing chief Tim Evans is expected to be in the running for the top post. The company confirmed that both internal and external candidates would be considered.
Industry watchers view Mackenzie's departure as a major blow to BT, coming at at time when rivals such as Carphone Warehouse and the cable giants are eating into its fixed-line business.
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