Barclays management has "concluded that new leadership is required" to accelerate an overhaul of the beleaguered group, it revealed in a statement on the surprise decision.
Jenkins has left the group with immediate effect, a spokesman confirmed to AFP. Chairman John McFarlane has been appointed executive chairman until a successor to Jenkins is found.
"I reflected long and hard on the issue of group leadership and discussed this with each of the non-executive directors," said deputy chairman Sir Michael Rake.
Jenkins replaced Bob Diamond in July 2012 -- who himself was forced to resign after the damaging Libor rate-fixing scandal.
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The retail banking veteran had vowed to bring a new culture of decency to Barclays, and oversaw drastic restructuring that shrank its investment bank.
He leaves the bank with 12 months' notice and will receive his current annual salary of 1.1 million pounds (USD 1.7 million, 1.5 million euros), as well as 950,000 pounds in "role-based pay" and a pension of 363,000 pounds a year.
Jenkins has however struggled to restore the group's damaged reputation which was also tarnished by forex rigging.
"In the summer of 2012, I became group chief executive at a particularly difficult time for Barclays," Jenkins said in a statement.
"It is easy to forget just how bad things were three years ago both for our industry and even more so for us."
He added: "I am very proud of the significant progress we have made since then. Our capital position is much stronger, our business model is more balanced, we are much more disciplined on cost management, we have made good progress in rebuilding our reputation and we are seen as a leader in the application of technology to our business."
The Libor system -- which has since been overhauled -- was found to be open to abuse, with some traders lying about borrowing costs to boost trading positions or make their bank seem more secure.
In another damaging blow, Barclays was slapped in May with a USD 2.4 billion fine by US and UK regulators for foreign exchange market manipulation.
Six major global banks, including Barclays and British peer Royal Bank of Scotland, were fined a total of almost $6 billion, mostly for rigging the foreign exchange market. Barclays' fine was the highest because it had not participated in an earlier deal.