Bailey is currently a non-executive director of bookmaker Ladbrokes and a governor of the English National Ballet School.
She was previously chief executive of newspaper publisher Trinity Mirror between 2003 and 2012.
Bailey has also held non-executive director roles at the Press Association, Littlewoods and EMI, serving as senior independent director at the latter.
‘Deep operating knowledge’
Gary Kennedy, chairman of Greencore, said: “Sly will bring deep operating knowledge, wide public company board experience and an energy and insight to our agenda.”
He added that her appointment completes the reorganisation of the board. Earlier this year Greencore appointed John Moloney, Heather Ann McSharry and John Warren to its board.
Meanwhile, earlier this month Greencore’s chief operating officer Di Walker announced her intention to stand down from her role on May 24.