During his daily coronavirus briefing, DeWine said Acton told him this week it was "time for her to step down."
She will stay in his administration as a chief health adviser, he said.
"She will continue to be able to serve the people of the state of Ohio in a very, very meaningful way, and continue to help me in a very meaningful way," DeWine said.
In her new role, Acton will continue to focus on the COVID-19 crisis, DeWine said, while advising on other health issues.
"Ohioans, you have saved lives. You have done this," Acton said during Thursday's briefing. "It is my honor to continue to work on this alongside you."
The health director also appeared in an animated parody of the "Laverne & Shirley" opening credits alongside DeWine. The animation, created by an Ohio freelance artist as a joke with friends, ended up going viral with over 1.2 million views on YouTube.
Acton was appointed health director in February 2019. She rose to prominence during the pandemic, often addressing the public during DeWine's briefings. She drew praise for her calm demeanor and the administration's swift, aggressive response to the coronavirus. But she was also the target of criticism as the state's lockdown stretched on.
Protesters demonstrated in front of her home on several occasions in May, and Republican lawmakers have been working on legislation to limit the health director's authority. In ruling that the state's order closing gyms during the pandemic violated the Ohio Constitution, an Ohio judge wrote that Acton acted in an "impermissibly arbitrary, unreasonable, and oppressive manner."
Lance Himes, the Ohio Department of Health's general counsel, will become interim director, DeWine said.