The former chancellor is in a leadership race with Liz Truss to become the next Conservative Party leader and PM, after Boris Johnson resigned.
It has also said C4 has been overly reliant on declining TV advertising.
But many members of the media industry have criticised the privatisation plans, which were announced earlier this year.
A campaign spokeswoman for Sunak has now confirmed: “Rishi will take forward Channel 4’s privatisation.
“Channel 4 is a crucial part of British broadcasting and supports our brilliant creative industries, but a lot has changed since the 1980s when it was set up to provide viewers with more choice.
“Privatisation will help Channel 4 to thrive in an age where they are also competing with Netflix, Amazon, Apple and many more.
“Standing still is not an option.”
The announcement was met with some disappointment in the industry.
Philippa Childs, head of broadcasting union Bectu, said it was “incredibly disappointing”.
She also warned that it would have “major consequences”.
“Channel 4 is a hugely successful public service broadcaster, consistently pushing the boundaries of entertainment and thought-provoking content for British audiences,” she said.
“This success is built on the back of the current model, which supports a thriving independent production sector and allows commissioners a degree of risk and creativity, of which the viewing public reap the benefits.
“Make no mistake – privatisation which will have major consequences for the UK broadcasting landscape, for the jobs of UK freelancers and for the UK’s creative economy.”
She added that they would "continue to fiercely oppose this destructive move".
The sale of Channel 4 has been backed by Culture Secretary Nadine Dorries, who is supporting Truss in the leadership contest.
Truss’ campaign spokesman has been approached for comment.
Additional reporting by PA.
Watch: Blur's Alex James cuts finger on Channel 4's Sunday Brunch