Dunne has been a member of the AFL Tribunal since 1997, but will step down from that role.
"We are delighted to have Emmett join the board. He brings a wealth of experience on many levels - not only as a result of his long association with elite and grass roots football - but through his distinguished career with the Victoria Police," Richmond president Peggy O'Neal said.
"He brings a particularly strong skill set in areas such as ethical leadership, culture and capability, integrity and security – areas of paramount importance in the modern game."