Tyler Sullivan, 31, of Bristol pleaded guilty in May to third-degree murder and endangering the welfare of a child.
Investigators say Sullivan shook his baby on at least eight occasions, leading to his death in May 2023.
On May 24, just after 11:30 p.m., police were called to Sullivan's home for reports of an infant in cardiac arrest.
The child died later that same day, investigators say.
Before being sentenced on Tuesday, Sullivan gave a lengthy, tearful statement, admitting "how guilty and ashamed" he was.
The child's mother and aunt submitted victim impact statements that were read during the hearing as well.
"My baby deserved to live a long, happy, wonderful life," the mother said.
She noted that she was too traumatized to ever return to her former apartment where she, Sullivan, and the baby had lived. She also said she had recurring nightmares about the day her son died.
The baby's aunt, in her victim impact statement, said her nephew's death left a "hole in our hearts that can never be filled."
Along with the prison sentence, a judge ordered Sullivan to undergo mental health treatment.