The 28-year-old suspect confessed to Austrian authorities that he killed Antonis Christofakis, 31, whose body was found in a ditch at a car park near Söll. It had 11 bullet wounds.
The lawyer of suspect Giorgos Vlachopoulos has said it was a crime of passion, as his client was having an affair with the victim's wife, a German citizen. Both Vlachopoulos and his lover face charges of premeditated murder and are in police custody.
Police in Munich say the victim's told them that her husband was violent towards her, and that she and her lover plotted to kill him so that they could live together. Police think they had been planning the murder for months, and then drove to Austria where they planned to dump the body in a ravine.
Austrian police found the key to a rental car with Christofakis's body. This led them to a car rental firm in Munich where they were given Vlachopoulos's name and the address of an apartment which turned out to belong to him. When police searched the apartment, thinking it belonged to the victim, they found the murder weapon. Austrian detective Walter Pupp said that "in the true sense of the word, the key found with the victim was ultimately the key to our success."
Christofakis had left his home in Siva, Crete, along with his wife and six-year-old daughter, to work in Munich.
28-year-old Vlachopoulos was arrested in Munich, but will be extradited to Austria.