Stinear, one of the league's most respected and successful figures, resigned as Melbourne coach after their preliminary final loss to premiers North Melbourne.
He coached the Demons to their 2022 premiership and, along with the Brisbane Lions' Craig Starcevich, is the only foundation AFLW coach still in charge of a team.
Given Stinear is a Surf Coast local, there had been plenty of speculation that he was headed to the Cats.
Former Geelong player Dan Lowther stepped down as coach last month, after five seasons in the role.
Geelong made the 2023 preliminary finals, but had missed the finals for the last two seasons.
Melbourne are one of the league's powerhouse clubs, making the top four in eight of the 10 seasons.
"Mick's extensive experience speaks for itself, he's had great success at the Dees building a program from its inception that has consistently been one of the top teams in the competition," said Cats chief executive Steve Hocking.
"His ability to mentor and build meaningful relationships and his credentials in developing talent will connect with our playing group as we build the foundations for 2026 and beyond.
"We're excited by Mick's vision for the next evolution of our AFLW program and the growth of our team."
Stinear will take over as Geelong coach next month.
"I will be forever grateful for having the privilege of helping to establish Melbourne's women's team," he said.
"I will cherish the relationships built over the years at the Dees and leave proud of the environment we created.
"I have a great respect for Geelong and look forward to building on the work of former coaches Paul Hood and Dan Lowther and working closely with the staff and players to deliver a high performance program that leads to a period of sustained success."
There have been significant post-season football department changes across the AFLW.
Adelaide, Richmond and Sydney will also have new coaches next season, with Ryan Davis taking over from Matthew Clarke at the Crows.
The Tigers sacked Ryan Ferguson a few months after re-signing him, having reviewed their underperforming women's program.
AFLW great Erin Phillips is now the head of the women's program at Gold Coast and Daniel Merrett has the same role at Port Adelaide.
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