Johnson was appointed to the role in January 2006 and said then that he would serve for three years.
Previously he had been chief executive of the international motor retail group from 1999 to 2006, during which period he changed the business strategy to focus on primary markets with selected manufacturer partners.
When Johnson stepped down as chief executive, Inchcape recruited former Euro Disney boss André Lacroix as his replacement.
Lacroix said: "Peter has overseen a fundamental change in the group, turning an international conglomerate into the world's leading car retailer, delivering significant value to shareholders along the way.
"It has been a real privilege to have served with Peter and to have benefited from his enormous industry experience."