A spokeswoman for the energy-saving lighting specialist said Mr McDonnell remains a shareholder “but is no longer acting in an executive capacity”.
Private equity firm ECI Partners won the race to acquire a minority stake in the Wakefield business in a hotly contested sale process in 2013.
Harvard has appointed Paul Hussey, who joins from another private equity-backed business, Strix Ltd.
Chairman Tony Clarkson said: “We are delighted to welcome Paul to Harvard.
“His broad experience and leadership skills, particularly in international markets, will support the company with its continued growth and expansion.
“We are all looking forward to Paul joining the business and making a positive contribution as we continue to deliver highly innovative lighting solutions for our customers.”
Harvard is a world leader in the design, development and manufacture of energy-saving lighting solutions. The company has stayed ahead of its rivals by investing heavily in R&D.
Its products include Leafnut, the award-winning wireless control and monitoring system for street lighting.
Mr McDonnell founded the business in his kitchen in 1993 with a design based on his university project. He could not be reached for comment.