The £75,000-a-year appointment was made by the FCA Board with the approval of the Treasury.
Tory Peer Baroness Manzoor will take up the role on 2 August, succeeding Sir Nicholas Montagu who is stepping down after more than seven years in post.
She was appointed to the House of Lords in 2013, where she served as House of Lords Government Whip and Minister between March 2018 and May this year.
Before joining the Lords, the Pakistan-born baroness spent over 20 years at board level within large, complex organisations.
She served as legal services ombudsman for England and Wales and legal services complaints commissioner.
While a member of the NHS policy board, Baroness Manzoor was one of eight regional chairs overseeing NHS operations and was involved in leading significant transformation programmes.
Charles Randell, chair of the FCA, said: “I’m delighted to welcome Zahida and I look forward to working with her.
“The Ombudsman Service fulfils an essential role in delivering a fair system for resolving disputes between consumers or small businesses and financial firms.
“Zahida brings extensive experience of public service, governance and dispute resolution to the role.
“Sir Nicholas is stepping down as he reaches the end of his final term after seven years leading the Board at the Ombudsman Service. I want to thank Sir Nicholas for his service over a period of significant change and wish him well.”
Commenting on her appointment, Baroness Manzoor said: “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.
“I very much see that continuing with the ombudsman service.
“I wish Sir Nicholas Montagu well as he hands me the baton and I look forward to working with Caroline Wayman and ombudsman service colleagues, who I know are committed to providing a modern and first rate service to all.
“And it’s vital too that we maintain effective and constructive relationships with all key stakeholders to ensure we all work together in the best interest of all users of the service.”
Sir Nicholas Montagu, Chair, commented: “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.
“But so too are our values of fairness and public service, and the dedication of our people who have achieved so much during my time here.
“Zahida is ideally placed to lead both that change and our future achievements and I wish her well in doing so.”