Allan criticised RNZ's culture and treatment of Māori staff during a farewell event for her then-fiancée.
"This partnership is a significant step for Newshub... we are very pleased."
"Murdoch profited off of fear and division with little apparent regard for warping the public discourse."
Amazon Prime Video will next year join streaming rivals in rolling out ads and introducing a higher-priced ad-free tier.
He will be replaced by his son, Lachlan.
RNZ said the resignation came after the company initiated an employment process with the journalist.
"We have tasked them to conduct a robust and comprehensive review of RNZ's editorial process."
ACT's David Seymour has called for an independent inquiry into the state broadcaster.
"Editorial independence here is very important."
