Benjamin Joseph Swann, 31, was expressionless as he entered the guilty plea in the Victorian Supreme Court on Wednesday afternoon.
He was previously charged with the baby boy's murder but that charge was withdrawn.
Swann instead admitted he killed the infant in circumstances that constitute manslaughter at a Werribee home in Melbourne's southwest in January 2024.
The boy's mother previously told a court Swann went to the boy's bedroom about 3am after hearing his cries on the baby monitor.
She said she heard a loud bang and then Swann entered the bedroom carrying her son and saying "take this f***ing baby before I kill him".
The woman said she noticed her son was wheezing and his colour had changed.
The boy was taken to hospital where he ultimately died after it was determined his brain injuries were non-survivable.
Swann originally pleaded not guilty to charges of murder and child homicide, and he was due to stand trial in the Supreme Court on October 23.
Justice James Gorton on Wednesday vacated that trial date, with Swann to instead face a one-day plea hearing on October 30.
Swann looked straight ahead as he entered his plea to child homicide, while the mother of his victim wiped away tears.
He was remanded in custody to his next court date.
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