The rules will also apply to less senior staff who could nonetheless do serious harm to a bank.
It comes two years after a parliamentary commission proposed a shake-up of the UK banking industry in the wake of the financial crisis.
The regime will take effect from March.
The new rules follow a public outcry after a series of scandals in the industry, including Libor rigging and foreign exchange rate fixing.
The Chancellor George Osborne said in his annual Mansion House speech last month: "The public rightly asks why it is that after so many scandals, and such cost to the country, so few individuals have faced punishment in the courts."
The Bank of England governor, Mark Carney, said at the same event that the "age of irresponsibility" was over as he set out new plans for jail terms for rogue bankers and traders who manipulate markets to be lengthened from seven to 10 years.
Earlier today, the former UBS and Citigroup trader Tom Hayes, who is accused of manipulating the Libor rate, told a court at his trial that senior managers knew what he was doing.
"I acted with complete transparency... My managers knew, my manager's manager knew. In some cases the CEO [chief executive] was aware of it," he said.
Mr Hayes is the first person to be prosecuted over the Libor scandal which cost Barclays Bank a then record Â£290m in 2012 before Royal Bank of Scotland  Â£390m for its part in the scandal.
The Financial Conduct Authority (FCA) and Prudential Regulatory Authority (PRA)  - part of the Bank of England  - said their new rules would place the "burden of proof" on top banking executives in incidents of wrongdoing within their companies.
The rules replace existing arrangements that require regulators to prove senior executives were responsible for wrongdoing.
FCA chief executive Martin Wheatley said: "Today we have given clarity on  rules that will embed personal accountability into the culture of the City. New conduct rules will add further momentum to improving standards across the industry."
The PRA's rule book sets out a list of key individuals to be held to account including chief executives, finance directors, chairmen and senior non-independent directors.
It means senior banking figures will be subject to a new "presumption of responsibility", meaning they will be guilty of misconduct if rules are broken in a part of a bank under their control.
The PRA will consider what they knew or ought to have known about the breach, scrutinising meeting minutes, email and telephone records.
Bankers will avoid punishment if they can show they took reasonable steps to avoid rules being broken, such as pre-emptive actions including reviews of the business.
A certification regime will cover staff who give investment advice as well as traders submitting benchmarks - such as for interbank lending rate Libor.
The FCA said it was consulting on expanding the latter to cover a wider scope of traders' activity.
Regulators are also proposing a new package of measures to formalise banks' procedures for whistleblowing.
British Bankers' Association (BBA) executive director Simon Hills said: "This new framework will help to restore trust and confidence in the banking industry damaged by the events of the last decade.
"A banking industry that sets the gold standard for accountability is good for customers and investors as well as those serving in it."
City regulators have published final rules that make top bank executives responsible for the misconduct of their employees -unless they can show they took steps to stop it.