The accused, 40-year-old Catalin C., faces charges of aggravated rape and murder over the death last November of a 27-year-old German woman who had gone for an afternoon run.
The suspect told the court in the southwestern city of Freiburg that he attacked the woman with a bottle and that he was "shocked" by his own actions.
"What I have done is unforgivable," he said.
He denied having a sexual motive for the crime, as alleged by the prosecution.
Prosecutors claim that Catalin C. raped the young woman and then beat her with an iron rod until she died. It took days and a large search operation before her body was found in the woods outside Freiburg.
Catalin C. was arrested in June and investigators have since said that forensic evidence links him to the unsolved murder of a 20-year-old French exchange student in the Austrian town of Kufstein in 2014.
The woman, from the French city of Lyon, was also raped before she was killed.
A verdict in the case of the German jogger is expected in late December.
Only once the German ruling is final can the accused be handed over to Austrian authorities to potentially face judicial proceedings there, a Freiburg court spokesman told DPA news agency.