"The video of Brendan's interrogation shows a confused boy who was manipulated by experienced police officers into accepting their story of how the murder of Teresa Halbach happened."
Wisconsin Attorney-General Brad Schimel said: "We hope the family and friends of Ms Halbach can find comfort in knowing this ordeal has finally come to a close."
The Wisconsin Court of Appeals upheld Dassey's conviction, saying the interrogation was not unduly coercive. Dassey had been read his rights, and his mother consented to the interview. Dassey did not have a lawyer present.
When Dassey appealed to federal court, a magistrate ruled in his favour, and a panel of the US Court of Appeals for the 7th Circuit agreed on a 2-to-1 vote.
But the full appeals court overturned that panel decision on a 4-to-3 vote in December.
"Dassey spoke with the interrogators freely, after receiving and understanding Miranda warnings, and with his mother's consent," Judge David Hamilton wrote. "The interrogation took place in a comfortable setting, without any physical coercion or intimidation, without even raised voices, and over a relatively brief time. Dassey provided many of the most damning details himself in response to open-ended questions."
The three dissenting judges called the decision "a profound miscarriage of justice".
"What occurred here was the interrogation of an intellectually impaired juvenile," wrote Judge Ilana Rovner. "Dassey was subjected to myriad psychologically coercive techniques, but the state court did not review his interrogation with the special care required by Supreme Court precedent."
At the Supreme Court, Dassey was represented by former US solicitor general Seth Waxman, who is a prominent practitioner before the court. He recruited an impressive lineup of former prosecutors and psychologists who told the justices that the interrogation was improper, and that the court should help clarify how juveniles, who can be easily manipulated and coerced, should be questioned.
But Wisconsin defended the conviction and said Dassey's case was not a good vehicle for the court to review the issue of juvenile interrogations.
Under federal law, the Supreme Court is to largely defer to decisions made by lower courts, and to intervene only if the decision by the state court was unreasonable.
Wisconsin said the state court followed Supreme Court precedent by looking at the totality of the circumstances and denied that investigators had fed Dassey facts of the crime to which he confessed.