Sean Michael Mullender, 22, from Connah's Quay, was due to go on trial accused of murdering baby Daniel.
He changed his plea at Mold Crown Court on Thursday and will be sentenced at a later date.
His son was admitted to the Countess of Chester Hospital on 2 October, 2014, but died two days later after being transferred to Liverpool's Alder Hey.
The prosecution told the court that it had accepted the manslaughter pleas on the basis that there had been an incident of shaking baby Daniel on the morning of 2 October.
A paediatrician's report indicated that the infant suffered brain injuries as a result of "severe rotational movement of the head".
There had also been two incidents of rib fractures - one previous and one recent - which were not related to the child's death.
Prosecutor Leyton Hughes said the manslaughter plea was being accepted on the basis that Mullender had no intention to kill or seriously harm his son.
The court was told that the decision to accept the plea followed discussion at the highest level within the Crown Prosecution Service, and with the extended bereaved family who had welcomed the decision.
The hearing was also told the defendant and the mother of the baby have since married.
Defending, Patrick Harrington QC said he would be seeking a pre-sentence report, and that he would also want the court to see "moving emails" between the defendant and his now wife as part of the mitigation.
Mullender was remanded in custody for sentencing until 28 April.
A Flintshire father has pleaded guilty to manslaughter after his two-month-old son died in October 2014.