Sir David was at one stage tipped to take over as governor of the Bank of England. As chairman of SG Warburg he negotiated its takeover by Swiss Bank Corporation in 1995. He will take over as non-executive chairman at Close at the annual meeting this autumn.
Rod Kent, chief executive, said yesterday that Mr Morley - one of five original members of the team that bought the bank out from Consolidated Gold Fields in 1979 - had planned to retire next year.
Mr Kent said: "We are very sorry Michael is leaving. But we have in Sir David someone of huge experience to draw on. He was enormously supportive of us in the early days. He personally gave us a lot of encouragement. We are hoping that the wealth of experience he brings will help us grow Close Brothers."
Sir David, who also holds non-executive directorships of J Sainsbury, Vodafone and the BBC, will continue his role as senior adviser to Warburg Dillon Read.
Mr Kent said the slowdown in the UK economy was continuing, although the climate had improved since last summer's "bloodbath" when the group warned it would not maintain its 24-year record of year-on-year profit growth .
Profits at the half year to 31 January were down by nearly 10 per cent to pounds 33.2m pre-tax, although Mr Kent insisted that the fall was on a period that in historic terms was "heroically good", and that the first half was ahead of last year's second half.
He said the group had also turned in a better trading performance than anticipated. Staff costs fell by 5 per cent in spite of an increase in the head count, reflecting lower bonus payouts overall. The dividend payout is 5.3p, up by 10 per cent. The shares fell 32.5p to 665p.