Hurd resigned after an internal investigation alleged he had made inaccurate expense claims and concealed a relationship with events contractor Jodie Fisher.
Hurd has denied making any advances towards Fisher. He has also insisted that he did not prepare his own expense claims and did not try to conceal his outings with Fisher.
Oracle has also appointed Hurd a director of the board, giving him a key supporting role to co-founder and chief executive Larry Ellison.
Ellison came out in strong support of Hurd last month, criticising the HP board's actions because it had found no truth in Foster's sexual harassment allegations.
"The HP board just made the worst personnel decision since the idiots on the Apple board fired Steve Jobs many years ago", he said in a letter to the New York Times.
Ellison said Hurd replaces Phillips, who had wanted to leave the company last December but agreed to stay on for a transitional period after the acquisition of Sun Microsystems.
As co-president, Hurd will take over Phillips' responsibility for sales and marketing, with additional responsibility for the company's 20 000-strong support organisation.
Oracle's other co-president, Safra Catz, will continue to oversee operations and finance, while Larry Ellison is to take charge of the company's engineering.
Hurd said the strategy of combining software with hardware will enable Oracle to beat IBM in both enterprise servers and storage, according to US reports.
Hurd's departure from HP came after five years in which he was praised by investors for his cost-cutting and strategic acquisitions in technology services and networking.
Analysts said Hurd's skills are a good match for Oracle, which is known for is aggressive acquisitions and cost-cutting.
Hurd's move to Oracle could rejuvenate the company's efforts to compete with HP, IBM and others in selling hardware, they said.
This story was first published by Computer Weekly