Mr Jenkins is currently in charge of Barclays Retail and Business Banking and has been a member of the the group’s executive committee since 2009.
The announcement is made just as the bank has been hit by more bad news.
Barclays disclosed on Wednesday that Britain’s Serious Fraud Office was investigating the bank in relation to events in 2008, when Barclays was raising money from Middle Eastern investors in the height of the global financial crisis.
Mr Jenkins made a statement saying he was “very proud to have been asked to lead Barclays”, and admitted the bank has made serious mistakes in recent years but now has an opportunity to restore its reputation.
Mr Jenkins will start on a basic salary of £1.1m, with a potential annual bonus worth up to 250% of his salary subject to performance.
In addition to this, he may also be eligible for a long-term incentive bonus worth a maximum of 400% of his salary.