Ferguson formerly held senior roles with KPMG, Bank of Ireland and Silverwood Property Developments Limited and is a qualified chartered accountant.
In his new role, he will chair the audit committee and will be a member of the remuneration and nomination committees.
Ferguson said: “I am pleased to be joining Dignity as an independent non-executive director for an initial six-month period.
“Dignity is a strong and caring organisation and I am looking forward to supporting its growth aspirations.”
John Castagno, chairman, Dignity, added: “We are delighted to welcome Graham to Dignity. He has extensive experience in finance and execution of growth strategies. Graham will add significant value to our board.”