Steven Dunne, 42, failed to return to Southview Low Secure Unit, Hellingly, at 17:00 BST on Wednesday.
After a police appeal on Saturday, Dunne later went into Bootle Street police station in Manchester, where he is in custody.
Dunne will return to hospital under a higher level of security.
Earlier, in their appeal, Sussex Police had said they believed he had gone to Manchester because he had family links in the city.
In November 2010, Dunne admitted the manslaughter of Gordon Stalker, 51, on the grounds of diminished responsibility and was detained indefinitely.
Sussex Police said the level of security he was originally detained under was approved by the Ministry of Justice.
After Dunne handed himself in, Lisa Rodrigues, chief executive of Sussex Partnership NHS Foundation Trust, said: "We were concerned for Mr Dunne's welfare and we worked closely with Sussex Police throughout their investigation."
The NHS trust had said Dunne posed a "low risk" after he was reported missing.
During the court case, Dunne, formerly of Chates Farm Court, Brighton, told Lewes Crown Court he believed Mr Stalker was controlling his mind and he could only be freed by killing him.
The pair were neighbours in a shared house in Elm Grove, Brighton, where they were friends and often socialised together.
But Dunne's mental health deteriorated and he began to believe that Mr Stalker was a witch who had captured his soul.
He stabbed Mr Stalker repeatedly in their communal hallway.
The judge ordered him to be detained under the Mental Health Act.
A paranoid schizophrenic who killed a former neighbour and went missing from his secure unit in Sussex has handed himself in to police.