Chevaze McGregor, 27, abused Jeremiah Regis-Ngawah over a period of months, Birmingham Crown Court heard.
The child was found by police and paramedics at an address in Wolverhampton in November.
The boy's mother, Sindyann Regis, 25, had previously admitted allowing the toddler's death.
McGregor believed in physical chastisement to "toughen children up" and used his fists and items such as a belt and a rod to discipline Jeremiah, West Midlands Police said.
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At a previous hearing, the court heard Jeremiah was found with head and body injuries when police and paramedics were called to an address in High Street, Wednesfield on 20 November.
The toddler, who had also suffered a bite wound, died in hospital the next day.
A post-mortem examination showed he died of abdominal peritonitis caused by blunt force trauma.
Det Insp Warren Hines, from the force's homicide team, said: "McGregor was a controlling, manipulative and violent individual.
"We believe the fatal assault was inflicted a couple of days before and Jeremiah was left in agony until he succumbed to peritonitis.
"Evidence shows that Jeremiah had defensive wounds to his hands and arms, which shows he tried to shield himself from the beatings."
Regis and McGregor, both of High Street, Wednesfield, will be sentenced at a later date.
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