The killer, Joakim Ericsson, was on trial for murders of Sölve Svensson, 64, and Irene Saldert, 58, who were last seen alive at their home in Båstad in mid-January 2007.
The court found Ericsson guilty of manslaughter for the killing of Svensson, but that he had committed murder in the killing of Saldert.
According to the district court in Helsingborg, the killing of Svensson was an impulsive act preceded by laughs and shoves which escalated into a brawl at the Hovs Hallar nature reserve northwest of Båstad on Sweden's southwestern coast.
In the killing of Svensson, the court found that no basis for assuming the killing was planned or that it resulting from a drawn out series of events. As a result, the court deemed the crime manslaughter.
However, the court stated that in the case of Saldert, there was more scope for Ericsson to have calmed down and considered his actions. In addition, the older woman did not pose a physical threat to him.
Evidence suggested that she was killed by several blows without having put up any major resistance. As a consequence, the court determined that to a certain extent, the crime was premeditated act and convicted Ericssson of murder in her death.
The trial marked the second time Ericsson has been on trial for charges related to the couple's disappearance, having first been arrested in March 2007 on suspicion of fraud after he sold the couple's car and took out large loans in Svensson's name.
Prosecutors were granted a new trial after the couple's mutilated and dismembered bodies were found in May 2008 in Häljasjön lake near Veberöd, 140 kilometres southwest of Hovs Hallar, in an area known to Ericsson.
The prosecution had requested for Ericsson to be sentenced to life in prison, citing the particular ruthlessness in his violent attacks on the elderly couple, who had no opportunity to defend themselves.
The defence charged that Ericsson was in a bubble and was not capable of assessing the consequences of his actions.
Ericsson's defence lawyer, Lars Tindberg, has not yet had the opportunity to read the 64-page verdict, but is satisfied that his client has not received a life sentence.
"It feels good. It was what we called for, that he would receive a fixed term of imprisonment," said Tindberg.
The district court ruled that the deaths failed to qualify as the "most serious cases of deliberate killing," which Sweden's Supreme Court has determined is a criterion for life sentences.
The highest fixed term of imprisonment that could be imposed when the offence was committed four years ago is 14 years in prison. Since Ericsson has already served one year in prison, the district court handed him a 13-year sentence.
"I have not gotten hold of my client, so I do not know how he feels. I cannot comment on a possible appeal until I have analysed the district court's various assessments," said Tindberg.