An investigation by the Financial Conduct Authority (FCA) and the Bank of England's Prudential Regulation Authority (PRA) sharply criticised Mr Staley's response to the receipt of an anonymous letter by the bank in June 2016.
The fine and public censure of the Barclays boss is unprecedented for a serving chief executive of a major bank.
Barclays said following Friday's announcement it would cut the value of Mr Staley's 2016 bonus by £500,000 - meaning that his acknowledged mistakes over the episode have cost him more than £1.1m.
The case centred on a letter, signed "John Q. Public", purportedly sent from a Barclays shareholder to the board making allegations of a personal nature against an "employee A" whose hiring at the bank Mr Staley had instigated.
The chief executive told the board the complaints against the employee were "historic".
He instigated an attempt through the firm's security department to track down the letter's author, discovering the date, time, location and cost of postage of the letter sent in the US and unsuccessfully trying to obtain video footage.
Mark Steward, FCA executive director of enforcement and market oversight, said: "Mr Staley breached the standard of care required and expected of a chief executive in a way that risked undermining confidence in Barclays' whistleblowing procedures."
Bank of England deputy governor Sam Woods said: "Protection for whistleblowers is an essential part of keeping the financial system safe and sound.
"Mr Staley's behaviour fell below the standard we require, resulting in today's fine and public censure."
The regulators have also made Barclays subject to special requirements meaning that it must report annually on how it handles whistleblowing, with senior managers responsible for the relevant systems and controls having to give "personal attestations".
Mr Staley said in a statement that he accepted their conclusions and the decision by the Barclays board to dock part of his 2016 bonus.
He added: "I have consistently acknowledged that my personal involvement in this matter was inappropriate, and I have apologised for mistakes which I made."