Joseph Ray violently shook tiny Ava Ray at their flat in Prestonpans on November 1, 2012.
The 32-year-old was charged after a near seven year probe into the death.
Ray had faced a murder accusation but prosecutors accepted his guilty plea to the reduced charge of culpable homicide on October 5.
On Wednesday, Ray was sentenced for causing the death of his daughter at the High Court in Glasgow.
Detective Inspector David Pinkney said: “My thoughts remain with Ava Ray’s family following this tragic event. I would also like to thank Ava’s extended family for their support throughout the investigation and I hope today’s result brings them some sort of closure.
“Ray took the life of his daughter. Just months old, Ava should have been safest in the care of her father - instead he inflicted injuries that she would never recover from.
“The investigation into Ava’s death was complex and intricate and I would like to thank all the officers and partners across all agencies involved who helped to secure the conviction and today’s sentence.”
Following his plea in October, the court was told little Ava had been born on September 3, 2012 and was the first child for Ray and his partner Lauren Scott.
Midwives had been "happy" at how they were coping with the newborn but prosecutor Ashley Edwards QC said the couple had arguments after the birth mainly over who would do night time feeds.
On the day of the killing, Ava was left in the care of Ray after her mother went to work in a local bar at 6.30pm.
An hour later, Ray unsuccessfully tried to get his aunt to come over to watch Ava while he went for a shower.
Around 10.50pm, Ray was then seen running to a neighbour after claiming he had found his daughter to be "cold to the touch".
Emergency services were called and Ray was told to carry out CPR before paramedics arrived.
Ava was rushed to Edinburgh's Royal Hospital for Sick Children where tests revealed her brain had been starved of oxygen.
Despite the efforts of a specialist team of medics, the tot tragically died the next morning.
Ava's death was initially treated as "unascertained", but Miss Edwards said that between 2014 and 2018 "various experts" were consulted about what had happened to her.
Miss Edwards said: "Following protracted discussions...the medical consensus is now that the pattern of injury...was caused by trauma."
It was concluded Ava had died due to a "head injury".
Ray had been held by police in October 2013 but was later freed and not charged with any offence.
It was in March 2019 that he first appeared in court in connection with his daughter's death.
The hearing was told that he initially claimed to police he had put Ava to sleep that night in her Moses basket.
Ray added he later went to give her a feed, lifted the baby up and found her to be "unresponsive".
No further details of the attack were revealed in court. At the time of Ava’s death, Ray had no previous convictions but he has since been found guilty of two "domestic assaults" on Lauren Scott.