He will join the bank as a non-executive director from 1 September and as chairman from 1 November.
Sir David currently works as a senior adviser to US bank Morgan Stanley and was previously chairman of Morgan Stanley International.
During his career he has held many high-profile positions such as assistant secretary to the Treasury, executive director at the Bank of England and deputy chairman at Lloyds Bank.
He has also carried out two independent reports on private equity and corporate governance and co-led the independent review that the Financial Services Authority produced into the failure of the Royal Bank of Scotland.

Mr Aguis said: "Barclays is fortunate to have attracted Sir David Walker to succeed me as Chairman. He will be taking over at a time when Barclays universal banking model is delivering a strong performance in difficult markets. I wish him every success as he leads Barclays through the next stage of its development."
Sir David said: "I am looking forward to joining the Barclays Boards and to playing my part in taking the company forward after recent events. The UK needs a strong financial services sector and Barclays has a crucial role to play in ensuring that this country has a successful, well-governed banking industry.
"My immediate priority, and critical to Barclays ongoing success, is the appointment of a new Chief Executive and I will be fully engaged in that process."