Liverpool-born John Shannon, 31, also stabbed his girlfriend's four-year-old daughter from a previous relationship before taking his own life.
The four bodies were found in a rented flat on 30 March, leading to the largest murder investigation in the British territory's modern history.
The inquest concluded the mother and children were unlawfully killed.
Shannon, a habitual user of drugs, thought he was being pursued by Lebanese contract killers that threatened to kill him and remove his organs, the hearing was told.
He also thought his Spanish girlfriend Anarda De La Caridad Perez Friman had tried to poison him and that he was not the natural father of their six-week-old baby Eve, whom he feared would be "pimped" by his imaginary pursuers, a psychologist told the hearing.
The family had been living on Spain's Costa del Sol, and had been in Gibraltar for a few days on their way to Britain.
The coroner's court was told that neighbours heard a woman's high-pitched screams and the desperate crying of a little girl on 28 March - the night they were killed - without being able to identify where the noises were coming from.
Shannon's victims were repeatedly knifed, and the mother and toddler had deep defensive wounds, indicating they had tried to fend off their attacker.
The court heard Shannon died two days later, on 30 March, from a self-inflicted cut across the neck that punctured his jugular vein.
Police found eight knives and a blood-soaked corkscrew in the flat, along with evidence of extreme violence in several rooms.
Coroner Charles Pitto concluded Shannon "took his own life while the balance of his mind was disturbed".
A man who fatally knifed his partner and their baby at a Gibraltar flat was mentally disturbed, an inquest heard.