Robert Hinz, who threw three-month-old Julian "vigorously" against a hard surface, will serve a minimum term of 21 years.
Julian suffered severe skull fractures last April and died in hospital when his life support system was turned off.
Hinz, 34, of Carysfort Road, Bournemouth, was convicted of murder by a jury at Winchester Crown Court.
The court heard Julian collapsed in a bedroom at home on 8 April 2016, when his mother was out shopping.
Hinz told the jury he tried to resuscitate his son, who was "floppy" and not breathing.
He had denied injuring his son, but police told the court he was "unable to control his anger and aggression".
Doctors identified a minimum of 42 fractures in Julian's body, including fractured ribs, inflicted by "squeezing" and bruising, the jury heard.
Following Hinz's sentencing, Det Insp Richard Dixey said the murder was a "truly appalling crime".
The court heard Hinz moved to the UK from Poland 2006, with wife Monika and their three children.
Julian was born a normal healthy child on New Year's Eve 2015.
Passing sentence, judge Mr Justice Warby said: "Over... three months until the fatal episode, you lost your job and ran into financial difficulties.
"Over the same period your son was subjected to serious violence at your hands on at least four occasions."
Mr Justice Warby said the harm Hinz caused to his family was "hard to exaggerate".
"My final words must be addressed to your wife," he said.
"The events will never leave her life, of course. With time will come some lessening of the pain. But she will be serving her own life sentence, because of what you did."
Bournemouth and Poole Local Safeguarding Children Board confirmed a serious case review was under way following Julian's death.
Chair Sarah Elliott said: "Following today's sentencing, a serious case review begun last year will continue, to determine if the decisions and actions undertaken by the various agencies involved during Julian's short life could have prevented his death and whether there are lessons to be learned."
A man who murdered his baby son in a "moment of anger" has been jailed for life.