Barclays finance director Chris Lucas and legal counsel Mark Harding are to stand down.
The news comes after Barclays admitted last summer Lucas was one of four current and former executives who were being investigated over the £7.3 billion Barclays raised from the Middle East in 2008 at the height of the financial crisis.
In a statement posted on the London Stock Exchange, Barclays made no connection between the investigation and Lucas' departure.
Barclays told the market both Lucas and Harding had agreed to remain in their roles until successors could be found.
In statement Barclays chief Antony Jenkins said: 'Chris and Mark both expressed to me late last year that they were considering stepping down from their roles at Barclays.
'The rationale which each shared with me was consistent and, typically, grounded in wanting to do what is best for the bank. Their decision to retire was theirs alone.'
Lucas added: 'It has been my great pleasure and privilege to serve as group finance director of Barclays for nearly six years now. While it has undoubtedly been the most eventful period during which anyone could have occupied a role such as mine, I have thoroughly enjoyed the challenge.
'However I think now is the appropriate time, as we start the implementation of the Transform programme, to begin my retirement from my role on the board and executive committee, and to pass the mantle on to a successor. I shall of course continue to give my full commitment to Barclays until he or she is appointed.'
Meanwhile Harding, who has served 10 years as legal counsel, said: 'We are starting a new period of the bank's development under Antony's leadership. I wholeheartedly support the direction of travel and have no doubt that great success lies ahead.'
The departures are the latest episode at Barclays as it tries to restore is reputation in the wake of the Libor scandal.
Jenkins is due to unveil the outcome of the bank's strategic review shortly, which will include the 'execution of change programme', which will take place over the next five to 10 years.