Operations director Jon Bridge will take over from Darby, who joined Brains in July 2018.
Derby has previously served as MD of Camerons Brewery, COO of Marston’s and CEO of Mitchells & Butlers.
Brains chairman John Rhys has also stepped down, with Andrew Winning, currently a non-executive director, taking over the role.
In December 2020, Marston’s announced a deal that will see it operate 156 Brains pubs in Wales, under a combination of leased and management contract.
Marston’s already has 106 pubs in Wales but plans to continue to operate the existing 156 Brains pubs under the Brains brand.
In January, it was reported the remaining beer brewing business could relocate to England, with a consultation on redundancies beginning.
Darby has said the Coronavirus pandemic had been 'absolutely brutal', with talks over closing the Cardiff brewery an inevitable consequence of the investment from Marston’s.
He said: “The important thing is that the family retain ownership of the beer and brand.
“We need to work out how to perpetuate the brand, which is very important to Wales, and we are likely to need to find a new location.
“If it is brewed elsewhere, it must be of the highest quality. It must be of the finest condition.”