Mr Marape was declared prime minister on Tuesday afternoon after receiving a unanimous 97 votes in the post-election parliamentary sitting.
He will lead a coalition of at least 17 parties.
His rival, former prime minister Peter O'Neill, sought to delay the sitting as some vote counting has not been finalised in the election which ran from July 4 to 22.
But the Supreme Court injunction was not successful.
Media have reported roughly 50 election-related deaths this year, down from 204 deaths documented in the 2017 vote.
Mr Marape said in a statement posted online he had a memorandum of understanding for a coalition of 17 parties, with his own Pangu Pati having the most members followed by the United Resources Party.
He said his main aim would be to stabilise and grow the economy, put in place sustainable debt financing and roll out government programs for education, health, and law and order.
"We will not be wasting time."
Mr Marape first became PNG's leader in May 2019.
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