Stone will take over from founding chairman Vic Cocker at a WRAP board meeting on 12 May and will work alongside chief executive Liz Goodwin.
Stone qualified as a lawyer after studying at Cambridge, and was then one of the founding directors of Close Brothers, the investment bank. He worked there for 23 years before leaving in 1998 and since then he has served as a non-executive director on the boards of companies including Smith & Williamson and Intermediate Capital Group.
He is currently on the board of DTZ Holdings and Opus Trust, and is a Governor of The King's School Canterbury.
Cocker is retiring, after holding the role since WRAP was founded in 2002. He said of Stone's appointment: "The board have selected Peter for his track record, his inclusive style, his vision and his obvious commitment to WRAP's mission.
"His experience of helping organisations grow, and guiding them through periods of change and development, is a very important attribute."
WRAP exists to help individuals, businesses and local authorities to reduce waste, recycle more and make better use of resources.
Waste reduction campaigner WRAP appoints new chairman
WRAP, the body that campaigns for a reduction in packaging waste, has appointed Peter Stone as its new chairman.