Hess's bones were exhumed at the graveyard in the small town of Wunsiedel, southern Germany, in the early hours of Wednesday morning.
The remains will be cremated and then scattered at sea.
Hess was captured in 1941 and sentenced to life in prison. He killed himself in jail in 1987 at the age of 93.
As he requested in his will, he was buried in the Bavarian town of Wunsiedel, where his family had a holiday home and where his parents were already interred.
The local Lutheran church which supervises the cemetery gave its permission for the burial at the time, ruling that the wishes of the deceased could not be ignored, the Suddeutsche Zeitung reports.
But they and local people have since become concerned by the number of far-right groups visiting the grave. Each year on the anniversary of his death, neo-Nazis have attempted to staged a march to the cemetery, saluting the grave, with its epitaph "I dared" and laying floral wreaths.
A 2005 court order banning such gatherings had little effect so the church decided to terminate the family's lease on the grave as of October 2011.
A granddaughter of Hess objected to the decision, the paper reports. She filed a lawsuit in an attempt to prevent it going ahead, but was eventually persuaded by the parish council to drop the case and allow the exhumation to go ahead.
Hess was one of Hitler's closest aides, but in 1941 he parachuted into Scotland in an apparently authorised solo peace mission, which was later denounced by the fuhrer.
He was imprisoned by the British for the duration of the war, and jailed for life at the Nuremberg trials in 1946. He spent 40 years in Spandau Prison in Berlin before being found hanged in his cell.
BBC News
