The former NSW premier informed fellow board members on Monday he would not seek re-election at next month's AGM, with David Boon to take over as interim chair.
The decision comes after Baird lost the support of Cricket NSW, with the country's most powerful state unhappy with the decision to allow private investment.
Baird had served as NSW's representative on the board, and approached them recently to confirm they would not support him in the current circumstances.
He did have the option of moving into an independent role, but AAP has been told Baird did not wish to continue without the support of all states.
Cricket Australia (CA) officials maintain that they continue to back the call for privatisation of clubs, which was confirmed earlier this month.
"After much consideration I have decided to stand down as CA chair and director," Baird said in a statement.
"I am delighted that David Boon has agreed to undertake the interim chair role while we complete the formal chair process, and I will undertake a transition process with David over coming weeks."
Baird had been on the CA board for six years, and served as chair since February 2023.
Alongside Todd Greenberg, he formed one of the most powerful duos in Australian sport.
In a statement on Monday, he again referenced the privatisation of the BBL as a positive for the sport.
"This year CA will report record revenue, profit, attendance and viewership, and most importantly a 40 per cent increase in participation over the past four years," Baird said.
"With recent decisions on the Big Bash I also believe the long-term sustainability is assured.
"I believe Australian cricket continues to be well lead by the CA board."
Baird's exit comes after Cricket NSW slammed the decision to allow privatisation earlier this month.
"This decision risks leaving cricket in NSW and Australia strategically and financially worse off, with direct consequences for our ability to invest in grassroots cricket," a Cricket NSW statement read earlier this month.
