Mr Speakman said the potential rewards outweighed the potential risks, adding he will not take an active role in the referendum or advise others on how to vote.
"I personally support a voice in the Australian constitution," he said in a statement on Saturday.
"There are no guarantees but other things being equal, working in closer partnership with Indigenous Australians - and elevating it by embedding it in the constitution - offers a better chance of closing the gap."
The Liberal leader previously made it clear he would allow opposition MPs to vote how they want on the issue.
He says he held concerns the voice to parliament could impede timely decision making but believes these have since been allayed.
With polls now showing the referendum only likely to succeed by a narrow margin, if at all, Mr Speakman called for changes to the proposal being put to the Australian people.
He urged the government to separate proposals for constitutional recognition and a voice into two different questions.
This week, WA Liberal leader Libby Mettam withdrew her support for the 'yes' campaign, saying the state government's scrapping of the Aboriginal Cultural Heritage Act had changed her mind.
"We have seen the repeal of a piece of legislation just weeks after it has been implemented as a result of an approach of providing the details later," she told ABCTV.
While acknowledging cultural heritage laws and the voice are separate issues, Ms Mettam said the plan of voting first and releasing details later is the same.
"I remain supportive of Indigenous recognition in the constitution," she said.
"What I was hopeful of - and what many Australians and Western Australians are hopeful of - is more detail on how the voice that has been proposed will lead to some real practical outcomes."
On Saturday, Mr Speakman called for the release of draft legislation on the voice, including detailing its proposed composition, functions, structure, powers and procedure.
The NSW top Liberal was not alone in putting off making public his position, with counterparts in Victoria and Queensland still to do so.
Victorian opposition leader John Pesutto has given coalition MPs the freedom to vote how they choose but is yet to reveal his personal position, as is Queensland opposition leader David Crisafulli.
Leader of Australia's sole Liberal government Tasmanian Premier Jeremy Rockliff, who is considered a moderate, plans to vote 'yes' in the referendum.
"Recent polling suggests the referendum is unlikely to succeed and that even if it does, it will only do so by a narrow majority," Mr Speakman said.
"Neither outcome helps our nation's ongoing journey of reconciliation.
"Whatever the outcome of the referendum, there remains the urgent business of reconciliation and closing the gap, to which we must all renew our commitment."
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