Adrian Sainsbury will take up the top role in September on a salary of £550,000 a year.
Mr Sainsbury has led the Close Brothers banking division as its managing director since 2016 and first joined the company in 2013 as chief executive of its commercial division.
In September last year outgoing chief executive Mr Prebensen announced he was resigning after ten years in the role, but has remained with the company since as it searched for a successor.
Mike Biggs, chairman at Close Brothers, said: "I am delighted to announce the appointment of Adrian Sainsbury as chief executive - his deep knowledge and experience, strong leadership and exceptional commercial expertise make him ideally placed to lead the group through the next stage of its development.
"Adrian's appointment provides continuity in the group's leadership team and business model, ensuring that that we continue delivering for our people, our customers, and our shareholders in the years to come.
"The board would like to thank Preben Prebensen for his outstanding leadership and very significant contribution over the last 11 years - he has overseen the transformation of the group over this period and leaves it in an excellent position operationally and financially and with a strong executive team."
Market turmoil driven by the global coronavirus pandemic saw client assets worth £1bn wiped from the asset management arm of Close Brothers earlier this year, with client assets dropping to £13bn by the end of April.
Despite this Close Brothers said its asset management division had delivered a "resilient performance" in the three-month period with an annualised net inflow rate of 10 per cent year-to-date.
The company did not furlough any of its staff during the crisis with the majority of employees set up to work from home.
Incoming chief executive Mr Sainsbury said: "I am honoured to be appointed chief executive of Close Brothers. Our group has a long and successful track record built on the experience and expertise of our people, strong customer relationships, and a prudent approach to managing our business.
"I look forward to taking this proven and successful business model forward in the years to come."
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