Denis Beytula fatally stabbed three-week-old Andrei Stefan at the family flat in Portland Close, Wallsend, North Tyneside, on October 2.
He has also admitted attempting to kill the boy’s mother during the assault.
Northumbria Police said the 27-year-old had grabbed a knife following an argument with the baby's mother, Andreea Stefan, 21, and began stabbing her and the infant.
She was able to call emergency services seconds later, the force added.
Woman, 44, whose large Dobermann dog mauled girl, 3, on Leigh Park street released back into neighbourhood by police
Woman arrested after little girl, 3, attacked by dog and left with 'life changing injuries' in Leigh Park
WATCH: This is the moment a man with a grudge fire-bombed a family's garden in Leigh Park
Man threatened with machete while washing car and assaulted in Portsmouth with police hunting two men
Four people hospitalised after 'serious' multi-vehicle crash involving lorry on A27 near Chichester
The father was arrested at the scene, while the two victims were transferred to the Royal Victoria Infirmary - where Ms Stefan recovered and Andrei died days later, on October 6.
Appearing in the dock at Newcastle Crown Court on Thursday, bearded Beytula showed little emotion as he pleaded guilty to murdering his baby and attempting to murder the boy's mother, who was his partner at the time.
He was told that he will be sentenced at the same court on December 19.
In a statement released following the guilty pleas, Detective Chief Inspector Dave Cole, of Northumbria Police, said Beytula had betrayed his victims ‘in the most violent of ways’.
He said: ‘This was a truly horrific assault that rocked an entire community and even now it is difficult to comprehend how Denis Beytula could commit these offences.
‘His victims were both completely innocent and they were two people he was supposed to love and protect - he betrayed them in the most violent of ways.
‘It is tragic when any life is taken away but it is particularly distressing when that life is a beautiful baby boy and I know that has had a profound effect on the wider community.’
Emergency services were called to the property at around 2.15pm on the day of the incident, where they found Ms Stefan and Andrei with critical injuries.
As the mother's condition improved in hospital, her son's worsened, and he was eventually declared dead.
Praising Ms Stefan, Mr Cole added: ‘She has been a pillar of strength throughout our investigation and I just want to take this opportunity to praise her for her incredible bravery at what continues to be a very difficult time.
‘Andreea fought for her life and, because of her determination, she is alive today to see this man put behind bars, but what happened that day will stay with her for the rest of her life.
‘Her world will never be the same again but we will continue to offer her all the support she needs so she can try and begin to move on with her life.’
In her own statement, Ms Stefan said: ‘I would like to take this opportunity to thank everyone who came to leave flowers and toys and paid respect to my son, in front of my house.
‘I really appreciate it and thanks to everyone for the messages, it's really nice to see how you guys support me and my family during this hard time.
‘May God give to everyone what they deserve. Thanks to all of you again.’