US Edition Gerald Corbett, the former chairman of Woolworths, will also join the board as a non-executive director. Both appointments are effective immediately.
Sir David will replace Michael Spencer, the Conservative Party treasurer and the chief executive of Icap. Mr Spencer disclosed last December that an investment group majority-owned by him used Numis shares as loan collateral without notifying the company.
A prolific director, Sir David led the sale of telecoms group 02 to Spain's Telefónica, where he still has a board position. He is also a non-executive director at Pearson.
Oliver Hemsley, chief executive of Numis, said: "I am confident that his experience in building successful businesses as well as working with Government will make a valuable contribution."
Sir David Arculus said: "I have watched Numis develop and am impressed with its principles, the quality of its people and prospects".