A merger would be the largest technology deal ever
HP chief executive Carly Fiorina told employees in a memo that the $20bn (£13.89bn) merger could now close in less than two weeks.
HP said the preliminary count showed that holders of 837.9 million HP shares voted in favour of the deal, compared with 792.6 million against.
Certification firm IVS Associates has spent close to a month counting proxy votes cast at an HP shareholders' meeting, although the firm itself refused to comment on the count.
The count supports HP's view, expressed bullishly at the time of the meeting, that shareholders were behind the firm's plans, despite vocal opposition from some key investors.
"We are eager to put this difficult period behind us and look forward to doing business as the new HP," Ms Fiorina said.
Buying vote allegations
The merger of tech giants ran into fierce opposition led by family heir Walter Hewlett, who has since been dismissed from the board.
Mr Hewlett said he would "examine and challenge" the count, and has the option to demand a recount.
He has already launched a lawsuit against the vote, claiming that Deutsche Bank, a key HP shareholder, was blackmailed into accepting the deal.
HP threatened to withdraw investment business if the bank did not comply, Mr Hewlett claims.
He also argues that HP misled investors about the progress of its merger integration plans.
But according to Reuters newswire, the 45 million share margin in the vote is just enough to seal the deal, even if Deutsche Bank's holding is ignored.
End in sight?
The final count is subject to a challenge process that could take another one to two days.
An HP spokeswoman said the company would have staff in the US state of Delaware ready to legally close the merger.
But Mr Hewlett is likely to ask for a court injunction barring the deal from closing until the trial is resolved, a source close to the disgruntled heir said.
Ms Fiorina said: "We waged this proxy contest openly, fairly and lawfully, and we won the merger on its merits."