The FCA and the Bank of England have been investigating Staley's links to the dead financier for two years.
Staley had business dealings with Epstein during his time at JP Morgan.
A statement from Barclays said: "Barclays and Mr Jes Staley, Group Chief Executive, were made aware on Friday evening of the preliminary conclusions from the FCA and the PRA of their investigation into Mr Staley’s characterisation to Barclays of his relationship with the late Mr Jeffrey Epstein and the subsequent description of that relationship in Barclays’ response to the FCA.
"In view of those conclusions, and Mr Staley’s intention to contest them, the Board and Mr Staley have agreed that he will step down from his role as Group Chief Executive and as a director of Barclays.
"It should be noted that the investigation makes no findings that Mr Staley saw, or was aware of, any of Mr Epstein's alleged crimes, which was the central question underpinning Barclays' support for Mr Staley following the arrest of Mr Epstein in the summer of 2019."
The FCA said: "The FCA and PRA do not comment on ongoing investigations or regulatory proceedings beyond confirming the regulatory actions as detailed in the firm’s announcement."
