The 24-year-old from Slovakia got the better of the world number five 6-1 6-2 in the semi-finals at the Rod Laver Arena in just over an hour.
Cibulkova was in control right from the start and broke Radwanska in the first game of the contest.
The 20th seed had two more service breaks and wrapped up the first set in just 37 minutes, hitting 10 winners compared to her opponent's six.
Radwanska won two games in the second set, but that did not stop the world number 24 from clinching it in just over half-an-hour.
Cibulkova, who becomes the first Slovakian to reach a Grand Slam final, will now take on Li Na for the title.