Gutherson and Cook will co-captain the Dragons in 2025, when the side will look to bounce back from their last-gasp capitulation from finals contention in Shane Flanagan's first season in charge.
Hunt had been the Dragons' talismanic halfback and captain before earning a release from the final year of his contract to join Brisbane for this season.
Blake Lawrie and Jack de Belin had filled in as skipper during Hunt's State of Origin duties in recent seasons, with the choice of the latter raising eyebrows given a high-profile court case that prevented him from contesting the 2019 and 2020 seasons.
In a media statement, coach Flanagan said it was a "clear choice" to bestow the captaincy on fullback Gutherson and hooker Cook.
Co-captain Clint Gutherson will be looking to lead St George Illawarra back to the NRL finals. (HANDOUT/ST GEORGE ILLAWARRA DRAGONS)
"Cooky and Gutho have both been really impressive in every facet since joining the club in November," he said.
"The difference each has made around the group with their professionalism, leadership, competitiveness, preparation and dedication has been obvious from day one, and having them share the captaincy is a clear choice.
"Each will bring slightly different things, but there's no questioning the positive impact each has made already."
Then 23, Gutherson was first appointed to Parramatta's co-captaincy in 2018 and had been either sole skipper or co-captain every season since earning a release ahead of 2025.
Cook captained the Prime Minister's XIII in last year's 42-20 win over their Papua New Guinea counterparts, and deputised as South Sydney co-captain for one game of the 2023 season.
The pair will be tasked with steering the Dragons to their first finals berth since 2018, with halfback Lachlan Ilias and back Val Holmes brought in to assist with that task.Â