A passer-by on Sunday discovered bobbing in Lake Traun in western Austria a first suitcase containing human remains, and a police dog then found a second one.
Police divers then found a third bag containing her head encased in concrete as well as the body of a man. The remains were identified as that of a woman aged around 70.
The man, whose body was found in around five metres (15 feet) of water, had two bags attached to his wrists containing "commercially available granite stones" and "personal tools," Austrian police said.
Autopsies suggested that the woman was strangled between December 25 and January 1 and that the man drowned some time later. There was no indication of involvement by a third party.
"We believe first and foremost that (the man's death) was suicide," state prosecutor Birgit Ahamer told a news conference.
The man and woman were later identified as a couple in their 70s from near Frankfurt in western Germany.