Bilevicius on Monday lost his appeal over a prison sentence handed to him in November by Skaraborg District Court over the murder of Lisa Holm.
The Swedish teenager's body was found days after she went missing in normally-tranquil and picturesque Blomberg near Lidköping in June last year, sparking one of Sweden's biggest manhunts for her killer.
"This means a lot for the family's grieving process. The family is incredibly strong and united (…) but this is something they will carry with them for the rest of their lives," her family's legal counsel, lawyer Tore Brandtler, told the TT news agency.
In its ruling the court repeated the district court's argument that forensic evidence, including traces of Bilevicius' DNA, strongly pointed to his guilt. It also noted that he lacked an alibi for the time of the murder.
Although an autopsy found that Holm had not been sexually assaulted, she was found partially unclothed and her mouth taped shut, and the appeals court said it believed his motive had been sexual.
"[He] is guilty of a sinister attack in a place which must have been relatively deserted at the time, and this against an individual who must have been unsuspecting and who lacked all chances of escaping," it added.
Bilevicius, a Lithuanian construction worker who lived in Blomberg at the time of the murder with his younger brother and wife, has denied any connection to the crime. His lawyer did not immediately confirm after the trial whether or not he would attempt to re-appeal the sentence to Sweden's Supreme Court.