They will also need to confirm they have "not knowingly mixed with anyone from South Australia" and take a Covid-19 test if deemed to be necessary.
It will be the first time residents of the country's two most populated states will be able to enter Western Australia since the borders shut on April 5 as a result of the coronavirus crisis.
McGowan said he would not hesitate to shut the border again under medical advice if there were future outbreaks in Australia's eastern states.
But he praised NSW and Victoria for their success in "getting the spread of the virus under control".
Victoria has now achieved 31 days without community transmission following its deadly second wave, and NSW is expected to reach the 28-day mark by the weekend.
"I know the last eight months have not been easy," McGowan said.
"I know the border arrangements have put pressure on families and have been hard to comprehend at times.
"As premier of the state I never thought I would bring in state border controls. It definitely has been an extraordinary year.
"I look forward to Western Australians being able to see friends and family from New South Wales and Victoria under our controlled border regime.
"My parents live in New South Wales so personally, for me, it is a relief to know that my parents are now safer at their home and hopefully I may be able to see them sometime in the future."
However, the WA border will remain closed to South Australia until December 11 at least, with the West Australian government to review that arrangement next week.
McGowan said people who drove from the eastern states through South Australia would not be permitted to enter Western Australia.
"You will then be treated as travelling from South Australia," he said.
"Anyone who has been in South Australia in the previous 14 days will then not be permitted to enter WA unless they meet an exemption criteria."
Today's announcement on borders comes after ABC medical expert Norman Swan sparked a social media outcry on Monday for tweeting it was "impossible to underestimate WA exceptionalism" regarding the border.
"They even believe that they've never been nett (sic) recipients of federal disbursements," Dr Swan tweeted.
"I say this as someone who loves the state. But you can tell a lot by how Western Australians drive. Can't change lane."
When asked about Dr Swan's comment on Monday, McGowan clarified with the reporter where Dr Swan lived, then quipped that it made sense.
"We've gone through lots of criticisms over the course of the last year … people in the east demanding this and demanding that," McGowan said.
"What we've done has worked. WA has supported the national economy."
McGowan said his government would continue to be cautious to continue it's virus record.
"If I listened to a lot of these critics over east, I would have shut down the mining industry and they would have lost all the income that WA provides," he said.
"If I'd listened to them over east, we would have pulled down the border and the virus would have come back from Victoria.
"Our own model has worked. We've had an open trading economy with the world that we kept operating; we've had a vibrant economy within WA.
"There will be critics all over the country. Mr Swan is the latest in a long line."
McGowan added that WA had been "enduring" criticism from people in the eastern states for about 150 years.
"A lot of people in the east aren't really educated about WA," he said.
"Many of the people in the east, I know for a fact, have never been here."
