Ex-Royal Marine Stephen Searle must serve at least 14 years in prison for the killing.
The judge, Mr Justice Green, told the 64-year-old defendant: “Your actions have caused devastating waves of pain and anguish to crash through your entire family.”
Searle was convicted of the murder by jurors at Ipswich Crown Court earlier this week.
The six-day trial heard the former politician rang 999 on 30 December last year and wished the operator a “happy new year” before confessing he had killed his 62-year-old wife Anne by “suffocation really, I guess”.
“Bit of a bizarre situation but you know… never mind,” he added.
When the operator asked whether it was just the two of them in the house, Searle replied: “Er… well just the one of us now.”
The couple’s marriage had been under strain since Mrs Searle discovered in June 2017 that her husband had been having an affair with their son Gary’s partner Anastasia Pomiateeva, prosecutor Andrew Jackson said.
Ms Pomiateeva was the mother of at least one of their grandchildren.
Searle’s “act of infidelity” had led to his wife’s death “one way or another”, Mr Justice Green told the court.
Officers attended the couple’s home in Stowmarket, Suffolk, within minutes of the 999 call and found Mrs Searle dead.
Mr Jackson said Searle had probably placed his wife in a choke hold – something he had knowledge of from his military training.
“The prosecution case is that on that Saturday night there had probably been yet another row between the two of them and in anger the defendant strangled his wife to death,” Mr Jackson said.
Forensic pathologist Dr Benjamin Swift said Mrs Searle would have lost consciousness after about eight to 15 seconds of pressure being applied to her neck.
Death required further sustained pressure for a period of minutes.
A post-mortem found Mrs Searle died of compression of the neck.
Searle claimed in court that he had been defending himself but his explanation was rejected by the jury.
Mr and Mrs Searle had been married for 45 years and had three sons together.
One of their children, also called Stephen Searle, said in a victim impact statement: “Not only have I lost my mum, but because of what he’s done I’ve lost my dad too.”
Searle showed no reaction to both the verdict and sentence.