The US private equity giant's proposed purchase of the casino operator had already been approved by authorities in NSW and Victoria.
Approval must still be granted by the Federal Court. A final court hearing is scheduled for Wednesday, Crown told the ASX.
Crown, along with rival Star, has been subjected to numerous inquiries that found widespread failings including money laundering at its Perth and Melbourne casinos.
Blackstone is one of the world's biggest private equity firms, boasting a diverse portfolio ranging from food and telecommunications assets to casinos.
The WA approvals were granted by Racing and Gaming Minister Tony Buti and the state's Gaming and Wagering Commission.
Mr Buti on Friday said Blackstone would be required to meet stringent conditions, including enhanced reporting of anti-money laundering and responsible gambling activities.
"The state government has already made significant improvements to the regulatory regime and remains committed to establishing an even tougher regulatory and governance framework to ensure whoever owns or runs Perth's casino is held to account," he said.
Shareholders of the listed casino operator voted to accept Blackstone's takeover offer last month.
Billionaire James Packer, who owns 37 per cent of Crown shares, stands to receive around $3.3 billion under the scheme.
Having stepped down as Crown's director in 2018, the looming sale will continue his retreat from public life. It will also mark the end of an era for the Packer family and its involvement in Australian public companies.
Mr Packer's investments in gambling and tourism came after he sold the media interests which his grandfather Sir Frank and father Kerry had controlled.
The 54-year-old last year told a WA royal commission there were "many oversights" during his time overseeing Crown's Perth casino operations.
Crown has been unable to offer gaming services in its new waterfront Sydney location because of restrictions on its licence.
The opening was at first delayed and then blocked after an inquiry by the gaming authority ruled Crown was not fit to operate. The NSW gaming authority has been working with Crown on plans for a conditional opening of gaming at the casino.
Victoria's casino regulator on Thursday issued a series of sale conditions, including a requirement that Crown Melbourne's board must be majority independent.
NSW Independent Liquor and Gaming Authority chairman Philip Crawford said Blackstone had been subjected to an extensive probity assessment.
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