Stone was most recently chief executive of Share plc, now part of Interactive Investor, where he was also finance director during the firm’s floatation on AIM in 2008.
Prior to Share plc, he was finance director at customer service consultancy Huntswood.
Stone will replace current chief executive Ian Sayers in October after a short handover period.
Elisabeth Scott, chairwoman of the AIC, said: “On behalf of the board, I am delighted that Richard has accepted this position.
"He brings a strong track record of leadership and business growth in the financial services sector.
"The board believes that Richard is well placed to build on the many successes achieved by the AIC under Ian’s tenure. Ian leaves with our grateful thanks and good wishes for the future.”
Stone added: “It is a real privilege to be taking on the role of steering the AIC, continuing the great work the association does to protect and promote the interests of its members and their shareholders.
“In my time at Share plc I saw first-hand the difference investment companies can make to investors’ portfolios and I look forward to working with all the team at the AIC in continuing to take that message to a wider audience.”
Sayers decided in March he would step down from his role after 11 years but agreed to stay on while the AIC searched for a new chief executive.
Sayers was appointed chief executive of the AIC in January 2010, having joined the association as technical director in November 1999.
During his time at the AIC, he campaigned for the abolition of commission on investment products which led to the Retail Distribution Review.
Since RDR was implemented in 2013, purchases of investment companies on adviser platforms have increased fivefold, the AIC stated.
He also spearheaded proposals for “reliable redemption” to avoid the problems that arise when daily-traded open-ended funds invest in illiquid assets, following the collapse of Woodford Equity Income last year.