His departure is part of sweeping changes being made by Lord Rockley, the group's new chairman who took charge last week, although Mr Agnew will not leave until later this year.
Kleinwort will start searching for a new chief executive in the next few weeks. The group will look from someone for outside the company, and possibly from outside the City.
A senior source said: 'What we need is somebody to pull the group together. We have good corporate finance, securities, treasury and financing operations and they need to work together.'
The departure of Mr Agnew, which is described as amicable, follows the retirement of David Peake as chairman earlier this year and has been brought about by the pressure for change that has been building within Kleinwort for some time.
Elements within the bank have been unhappy that the planned alliance between Kleinwort, Banque Nationale de Paris and Dresdner Bank, first proposed nearly three years ago, has not come off despite BNP taking a 4.7 per cent stake in Kleinwort in 1991.
'We have been lacking direction, lacking a clear strategy of how to take on the likes of Warburg, Goldman Sachs and Morgan Stanley,' one said.
With the announcement of Mr Agnew's departure, there is likely to be a substantial reorganisation of the group's management structure.
Insiders said this is expected to bring more power to Simon Robertson, the group's well-respected deputy chairman who worked closely with Lord Rockley in the corporate finance department, most notably when they pushed through a rights issue and a management restructuring at British Aerospace.
Mr Agnew, 51, was educated at Eton and Cambridge. He has been chief executive of Kleinwort for five years, presiding over the integration of stockbroker Grievson Grant and the creation of one of the City's leading market-making teams.
However, the securities side has not been able to make a large enough contribution to profits to satisfy Kleinwort's critics.
It has been struck by various mishaps, the largest of which was a pounds 34m loss when the group failed to place a 29.9 per cent stake in the oil group Premier Consolidated.
The company has also had problems on its banking side, particularly in the US where it has suffered from a large exposure to highly leveraged transactions and an embarrassing loss from investing in a business venture run by the head of the group's Los Angeles trading operation.
Kleinwort has shown signs of recovery, with its pre-tax profits for last year beating market expectations with a 66 per cent increase to pounds 46.3m. But close watchers have noted that the results were flattered by a decrease in bad debt provisions.
Mr Agnew is believed to have received pounds 371,000 in salary, bonus and pension payments last year, making him the highest-paid of Kleinwort Benson's directors.
He is believed to be on a three-year rolling contract and may be entitled to compensation for loss of office of about pounds 1m.
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