Before Danone, Bailey held senior marketing roles with Pepsico, Campbell Arnotts and SC Johnson and Son.
In the marketing role with a2 Milk, Bailey will be responsible for managing the strategic and creative direction of the a2 Milk brand, developing integrated marketing programmes and leading consumer insights and product innovation, the company said.
Chief executive David Bortolussi said Bailey's appointment was an "excellent fit" from a leadership and cultural perspective.
"It is essential that we continue to invest in and strengthen the a2 Milk brand to enable us to return to growth in our core business and to capture new opportunities through innovation and new product development," he said in a statement.
Bailey will start her role later in 2021, with her start date yet to be confirmed.
In the meantime, Janelle Tong, a2 Milk's group head of marketing, will take up the job until Bailey starts.
Shares in a2 Milk last traded at $6.70, up 7 cents on the day. The stock hit a record last July of $21.51 and slumped a low last month of $5.50.