It comes as Newcastle signed Kalyn Ponga to a new contract extension that keeps him at the Knights until the end of 2030.
After weeks of speculation, the last-placed Dragons confirmed livewire fullback Drinkwater would join from 2027 on a three-year deal.
The acquisition is a major boost for a team that has lost their first seven games of 2026 and fired coach Flanagan on Monday.
The Dragons have not played finals since 2018 and have lacked attacking direction since Ben Hunt's departure at the end of 2024.
Drinkwater, known for his electric running game, is set to help remedy both of those problems and most recently guided the Cowboys to victory over perennial contenders Cronulla on Friday night.
The 28-year-old's move is a showing of faith in the Dragons, who have not settled on a coach for next season and begin life under interim coach Dean Young in round eight.
Drinkwater joins South Sydney forward Keaon Koloamatangi as one of two big signings for 2027.
His arrival is set to push co-captain Clint Gutherson out of fullback and likely into the outside backs next season, with Gutherson himself endorsing this move in recent weeks.
"I'm really looking forward to joining the Dragons and being part of what the club is building," Drinkwater said.
"You can see the young talent from the area making its way through the ranks, so it's an exciting challenge to go on this journey with them.
"I look forward to finishing strong at the Cowboys this year and then arriving at the Dragons for 2027 to do everything I can to contribute to the team's success."
Unable to find regular NRL opportunities at Melbourne, Drinkwater has played all but one of his 152 games since relocating to the Cowboys in 2019.
He was a member of the Cowboys team that came within a converted try of a grand final berth in 2022.
Drinkwater had been linked with an exit from the Cowboys in recent weeks given the club's intentions to prioritise Jaxon Purdue as a playmaker of the future.
Ponga is set to play into a 13th season at the Knights after committing his future long-term on Saturday.
The Queensland representative has been the club's most critical player since arriving from the Cowboys in 2018 and won the Dally M Medal for his excellent 2023 season.
Ponga's new deal signals his support for the Knights' direction under new coach Justin Holbrook, who has taken the reigning wooden spooners to a 4-3 record through seven rounds.
He had been linked with a possible move to rugby union late last year but will now remain at the Knights past his 32nd birthday.
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