Roger Cook is set to become Western Australia's 31st Premier.
Health Minister Amber-Jade Sanderson was in the race for the top job but withdrew late on Tuesday after Transport Minister Rita Saffioti backed Mr Cook.
Ms Saffioti is expected to serve as Deputy Leader.
On Monday, Mark McGowan resigned as Premier and Member for Rockingham after six years at the helm.
“The truth is, I’m tired, extremely tired. In fact, I’m exhausted,” McGowan said.
"I just don't have the energy or drive to continue in the role as Premier."
Mr McGowan will officially step down on Friday while Mr Cook is likely to be sworn-in on Tuesday.
Early voting for Secret Harbour by-election begins Monday
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