The 47-year-old who was born in Germany and played for the Black Stars in their first World Cup finals appearance in 2006, replaced the sacked Milovan Rajevac in February, initially as interim boss, and was given a deal until the end of December.
He also has the role of talent coach at Bundesliga side Borussia Dortmund.
“I said before, it was clear I would stop after the World Cup. At the moment, me and my family see our future in Germany, I like my role at Dortmund,” coach Addo said after Ghana exited the tournament following a 2-0 loss to Uruguay at the Al Janoub Stadium.
“I said I would resign after the World Cup even if we were world champions.”
Ghana finished bottom of Group H with three points after losing to Portugal and Uruguay, having beaten South Korea in between.
Coach Otto Addo’s departure means Ghana must move quickly to get a new coach in place before they continue their Africa Cup of Nations qualifying campaign in March.
He joins Roberto Martinez (Belgium), Carlos Queiroz (Iran) and Gerardo Martino (Mexico) as coaches who immediately left their jobs after World Cup elimination this week.