Mr Lam, currently the company’s managing director, will replace Mr Fitzgerald on Wednesday (6 September).
As part of a phased retirement, Mr Fitzgerald will hold onto his responsibilities as finance director for the time being.
Before being appointed chief executive in 2007 Mr Fitzgerald had served as finance director for eight years.
David Gelber, chairman of Walker Crips, said: “Rodney has done a tremendous job in leading the business for over 10 years as CEO and has played a pivotal role in managing the transformation of the group from private client stockbrokers into an integrated investment and wealth management house.
“His successor, Sean Lam, has already played a key part in the success of the group, previously as CEO of Walker Crips Stockbrokers Ltd and as group managing director with dual responsibility over group operations and technology, making him the ideal person to lead Walker Crips into the future.”
Mark Rushton, the company’s chief investment officer, will assume responsibility of the investment management and stockbroking subsidiary Walker Crips Stockbrokers as its chief executive, subject to FCA approval.
Mr Lam said: “Our firm has been serving clients for an incredible 103 years because of the dedication of our investment managers.
“In today’s era of dramatic technological change, we are now positioned to engage a higher gear, a higher level of intensity, a different mindset and to be a 'technology driven financial services company’ creating new offerings to clients, value to shareholders and greater opportunities for our staff.”