The American will step down as chief executive of retail and business banking (RBB) in Britain and Europe on 1 October.
She will stay on as vice-chair of the division until the end of the year.
Ashok Vaswani, currently chief executive of Barclays Africa, has been named head of RBB for Britain. Antony Jenkins, RBB chief executive, also takes on responsibility for Europe.
Oppenheimer, 53, spent six years with Barclays and has been credited with driving the integration of more than one million customers from Woolwich, which the bank took over in 2000. She is now understood to want to take up roles outside financial services.
She said: “When I came to Barclays my goal was clear, to lead the transformation of UK retail banking and leave in place a successful management team that is well placed to continue the journey. It is with immense pride that I leave having achieved this goal.”
Jenkins praised her work on the turnaround of Barclays in Europe.