A spokesman for the firm, which recently merged with Compaq, said job losses would be "minimal".
The spokesman said: "I can confirm that HP are leaving the Pinewood site. Following the merger with Compaq, the decision was taken to move all staff and operations to the Bracknell and Reading sites.
"This is really part of our ongoing integration process and is understandable considering the number of other offices in close proximity.
"There will be an absolute minimum of redundancies as the vast majority of staff will be relocated to these other offices in Bracknell and Reading.
"This is not a job-cutting exercise, it is a consolidation exercise."
She added that the company was "anxious to get things moving", and that the first group of employees would be relocated in November and December.
The move is expected to be completed by the first half of 2003.
Crowthorne MP Andrew MacKay received the news of the closure with caution.
He said: "Ever since the merger of HP and Compaq in May, we have worried about inevitable redundancies.
"I am particularly sad that HP is planning to leave as the company has a long association with Pinewood.
"I shall be working carefully to ensure that any of my constituents who are made redundant receive a fair compensation package."