Garry Lockhart, 33, strangled his wife Janet at their home in Bonnyrigg, Midlothian, after an evening out drinking with friends on December 28 last year.
After a few hours’ sleep, he then woke and smothered his two-year-old son Michael.
Sentencing Lockhart at the High Court in Edinburgh today, Lady Wise jailed him for life with a minimum of 25 years behind bars.
She said: “Your actions have devastated your family and in particular your parents-in-law who have lost a precious daughter and a grandson to whom they were devoted.
“Nothing can be said today that will alleviate in any way the incalculable loss that they and all those who knew and loved Janet and Michael have suffered.”
In her statement, posted on the Judiciary of Scotland website, she said Lockhart had shown no regard for the “immeasurable value of their lives”.
She added: “To murder a vulnerable child who trusted and depended on you was a particularly wicked, unfathomable act. Your actions now require the imposition of a severe punishment.”
Lockhart had pleaded guilty to the murder of his wife and the culpable homicide of his son on the grounds of diminished responsibility, but this was rejected by the Crown. He was instead found guilty on September 18 of both murders following a trial at the same court.
The trial heard that Lockhart attacked his 29-year-old wife after she raised concerns that he was not in a fit state to look after their son while she was out at work.
He then hatched a plan to kill his son and take his own life.
Lady Wise said: “You did not kill Michael immediately after you murdered your wife. You fell asleep for some hours, were awoken by your son in the morning and then deliberately in the cold and more sober light of day first played with Michael, then put a pillow over his face and, when he struggled, put your hand over his nose and mouth until he could no longer breathe and died.
“This, the jury determined, was murder.”
The Crown Office said Mrs Lockhart had been due to start work at 4am and concerns for the family grew throughout December 28 after she did not arrive.
Police were called and forced entry to the South Chesters Lane house, where they discovered the bodies of the mother and son.
Lockhart was found in a parked car in a layby on the A703 later that evening.
John Dunn, procurator fiscal for the east of Scotland, said: “Garry Lockhart strangled his wife and smothered his infant child in their own home.
“This is nothing short of a tragedy and our thoughts are naturally with the family and friends of the victims.
“I would like to thank all those close to the family who came forward to help police and prosecutors piece together the case against the accused.
“By virtue of that co-operation it has been possible to ensure that Garry Lockhart has been brought to account for his appalling deeds.”
Detective Chief Inspector Scott Cunningham, from the Major Investigation Team, said: “I acknowledge the sentence of Garry Lockhart but my thoughts are first and foremost with Janet and Michael’s family, who have been devastated by his incomprehensible actions.
“No sentence can alleviate their pain and I would like to pay tribute to them for their immense dignity and strength throughout the investigation and trial.”