The vote was the first business of the day.
The three-term MP, from Morobe Province, was declared with 55 votes, defeating former Parliament speaker and Nawaeb MP Timothy Bonga, who collected 36 votes in the second secret ballot vote.
The other nominee, former Rigo MP and PNGDF commander Edward Ranu Diro, was eliminated in the first round of the secret ballot voting.
Dadae is another serving parliamentarian voted to occupy the vice-regal office.
The term of the current Governor-General Sir Michael Ogio expires at the end of this month.