Amanda Knox and Raffaele Sollecito were convicted for the second time in 2014.
The Italian top court must now choose whether to confirm the conviction or order a retrial.
Amanda Knox and Raffaele Sollecito have maintained their innocence throughout and have already served four years in prison.
Meredith Kercher, 21, was found dead in the flat she shared with Amanda Knox, now 27, in Perugia, central Italy, where both women were studying.
Her body was found under a duvet in her bedroom, which had been locked from the inside.
Prosecutors claimed Meredith Kercher was killed by Amanda Knox and Raffaele Sollecito, 30.
They were convicted of murder in 2009 after a trial in Perugia.
Amanda Knox and Raffaele Sollecito were freed in 2011 after an appellate court overturned the convictions.
The Court of Cessation rebuked the appellate judge’s reasoning and last year an appeals court in Florence sentenced Amanda Knox to 28 years and Raffaele Sollecito to 25 years.
Raffaele Sollecito, from Bari, southern Italy, has remained in the country, but a definitive conviction would trigger attempts to extradite Amanda Knox who lives in Seattle.
Rudy Hermann Guede, born in the Ivory Coast, who opted for a fast-track trial, is serving a 16-year sentence for his role in the murder.
The high-profile case has inspired books and at least two movies, and Kercher’s family has said Meredith, the real victim, risked being forgotten.
Originally portrayed as a fast-living partygoer, Amanda Knox came to be seen in much of her home country as a victim of a botched investigation and an unwieldy justice system.
The US state department has said officials are monitoring the case.
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