The brief is believed to include above-the-line elements and will promote the Advanced Micro Devices brand, which is the world's second-largest microprocessor and rival to the market leader, Intel.
The work is believed to use Modem's international offices, but will be led by its London operation.
The account was previously shared between McCann Erickson and DraftFCB. DraftFCB is understood to have taken on responsibilities for HP's AMD-related work because of McCann's conflict with the Intel account.
The appointment comes just three months after HP gave Modem Media the task of revamping its network of websites across Europe, the Middle East and Asia.
Earlier this month, it also emerged that HP's procurement department was reviewing DM agencies for a remit that covered Europe, the Middle East and Africa.
Modem refused to comment on the news.