Meggs will take up his post for a three-year term in May, replacing Lorraine Baldry who has chaired the board since May 2018.
Sellafield is a subsidiary of the Nuclear Decommissioning Authority and Meggs will report to NDA CEO David Peattie.
Peattie said: “Tony brings a huge breadth of leadership experience and his insight on major infrastructure projects and the energy sector will be invaluable to Sellafield.
“I look forward to working with him and know he will have a significant impact on Sellafield Ltd.
Significantly, Meggs held several senior roles at BP and as Head of Technology was responsible for the organisation’s central project and engineering functions and R&D.
He co-founded the BP Projects Academy, building a cohort of leaders to maximise the success of the organisation’s global projects, which later became the inspiration for the Government’s Major Projects Leadership Academy.