Ms Sanderson said she had decided to withdraw "in the interests of unity and stability" after key powerbrokers swung their support behind a ticket led by Mr Cook with Transport Minister Rita Saffioti as his deputy.
"As I said this morning, my plan was to talk to my colleagues," she said in a statement on Tuesday.
"I have now done that, and in the interest of unity and stability I will not be nominating for the leadership of WA Labor.
"I am fiercely proud of everything that this Labor government has achieved over the past six years.
"I respect the process, and the views of the entire WA Labor team."
Mr Cook, who has served as deputy premier since Labor came to office in 2017, is poised to become the state's 31st premier.
The 57-year-old served as health minister at the height of the COVID-19 pandemic before assuming his current portfolios of state development, jobs and trade.
A protracted leadership battle had loomed before Ms Saffioti met with Mr Cook on Tuesday and agreed to serve as his deputy.
A group of 17 MPs aligned with the Australian Manufacturing Workers Union threw their unanimous support behind the ticket, shifting the majority of the left faction into his camp.
"The deputy premier and I have been parliamentary colleagues for 15 years and cabinet colleagues for six years," Ms Saffioti said in a statement.
"What we offer above all else is stable leadership, which is what our state needs right now.
"The deputy premier and I will continue to engage with our parliamentary colleagues as we seek to deliver unified and stable leadership for the state and a consensus ticket for the party."
Emergency Services Minister Stephen Dawson said the AMWU believed Mr Cook had the necessary experience to serve as premier.
"Certainly one of our strengths as a government has been how we dealt with COVID-19," Mr Dawson said.
"Roger, of course, was a big part of that.
"Amber's a fantastic minister.
"She's been a minister, though, for just over a year and a half.
"She's got a big task ahead in the current portfolio that she's got."
Mr Dawson played down talk of disunity within Labor's left faction and backed Ms Sanderson to one day lead the party.
"I'm confident that if Roger becomes the next premier of Western Australia, there won't be divisions," he said.
Ms Sanderson became a cabinet minister in 2021, taking the environment and commerce portfolios before stepping up to health during a meteoric political rise.
She had earlier won the backing of a majority of the roughly two dozen MPs affiliated with the United Workers Union.
Her withdrawal from the leadership race means the party is likely to avert having to canvass rank-and-file members across several weeks.
The entire parliamentary party is expected to meet early next week.
Mr Cook earlier made a public pitch for the job, saying he had the necessary energy, experience and support of his colleagues.
"As someone who's been acting premier on many occasions, I feel I know what is required to be premier," he told Perth radio 6PR.
Mr Cook said he had only learned of Mr McGowan's shock decision to resign at a cabinet meeting on Monday shortly before it was announced.
Mr McGowan said the role of political leadership was relentless and the COVID-19 years had exhausted him.
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