The partnership, which began in 2000, saw HP provide technology and sponsorship for the F1 team.
It is believed that HP backed out of the sponsorship deal because BMW is splitting with Williams and buying the Sauber team in January. From next season, Williams will have engines supplied by privately owned Cosworth, formerly part of Ford, and is not expected to not perform as well as in previous seasons.
This, coupled with the fact that HP announced it was shedding almost 1,000 jobs in the UK on Tuesday, made it unlikely HP would feasibly continue its F1 sponsorship.
In a statement, Cathy Lyons, HP's executive vice-president and chief marketing officer, said: "We have met our objectives and it is a natural moment for HP to conclude our relationship. We wish [Williams] all the best as they go in a new direction next season."
Since the HP sponsorship started five years ago, Williams has won more than 10 Grands Prix and finished second in the Constructors Championship in 2002 and 2003.
Separately, enery drink giant Red Bull is set to buy the Minardi Formula 1 team and use it to showcase drivers in its young driver scheme.
The soft drinks company, which bought the Jaguar team from Ford last November and renamed it Red Bull Racing for this year's season, will take control of Minardi on November 1.
Minardi owner Paul Stoddart hailed the agreement as "good news" for the team, which he bought in 2001.
Red Bull will run two Formula One teams from the start of the 2006 season onwards.
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