Zahida — who will take up the post on 2nd August 2019 — spent over 20 years at board level within large organisations before joining the Lords.
She has served as both the legal services ombudsman for England and Wales and the legal services complaints commissioner.
She will succeed Sir Nicholas Montagu, who is stepping down after more than seven years.
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“The Ombudsman Service fulfils an essential role in delivering a fair system for resolving disputes between consumers or small businesses and financial firms,” said Charles Randell, chair at the FCA.
“Zahida brings extensive experience of public service, governance and dispute resolution to the role.”
Zahida added: “My appointment to the role of chair of the Financial Ombudsman Service follows a career dedicated to public service and ensuring fair treatment in people’s everyday lives.”
Commenting on his departure, Nicholas said: “‘I am really pleased to be handing over to Zahida Manzoor.
“Our organisation is very different from the one I joined seven years ago, and change is a continuing theme.”