Some 77 percent of those who are members of the Unite trade union said they wanted to strike, and 85 percent also support other additional industrial action.
The action concerns 150 customer service engineers and support specialists, who are home based and operate across the UK.
The workers' complaint is around being transferred on 1 November into the HP CDS business, which was formed from the acquisition of Synstar in 2004. Alongside the move they are losing pay and pension benefits, including a ?2,000 (US$3,336) performance bonus scheme and a final salary pension, Unite said.
Unite said the workers were being treated with "contempt", and that HP was "taking the opportunity of weaknesses in current employment legislation" to remove the pay and pension benefits.
The union will meet with senior representatives at HP next week, to decide on the timing of the strike and the form of other industrial action to be taken. It said there was an "absence of any attempt" by HP to address the pay and conditions issues.
HP is facing other possible strike action after it was announced on Tuesday that staff at EDS, who are now employed by HP, are voting in a strike ballot over upcoming job losses. Most of the 1,000 staff, who are members of the PCS union, work on a series of IT contracts at the Department for Work and Pensions.
Peter Skyte, Unite national officer, said today's ballot was "likely to be the first of more industrial action in HP, unless the company rethinks its policy of attacking the terms and conditions of its workforce".
HP insisted it "respects" the rights of its employees to be part of a union, adding that it will "maintain a dialogue" with the body. But Unite said the company was guilty of "crass actions" in trying to "undermine the union" by dealing with employees individually, instead of as a group.
