Mother-of-three Wendy Mann, who was 26, was found dead in her flat, in Chapel Street, Black Lake, West Bromwich, in August 2015 having been strangled.
Her ex-partner Leroy Sterling, 63, was on trial accused of murdering her and attempting to kill her new flame Trevor Tyndale six weeks earlier.
He denied the charges but was today found guilty at Wolverhampton Crown Court on both counts.
In a family statement read out in court relatives called Miss Mann's death 'mindless and selfish'.
They said: 'Wendy is simply irreplaceable'.
After the hearing West Midlands Police released CCTV showing during the trial of Sterling carrying clothes from the home of Wendy Mann in the Carters Green area of the town.
Speaking outside court, Detective Inspector Martin Slevin, who led the investigation, said: "Wendy Mann was a loving mother to three children whose live was cruelly ended by the father of those children, Leroy Sterling.
"Despite them not being in a continuing personal relationship or living together, Sterling upon finding out that Wendy was having a relationship with another man visited her flat.
"No one, but Sterling, knows exactly what subsequently took place but what did follow was obviously a vicious attack upon Wendy by Sterling that ended her life.
"This was no doubt driven by a jealous rage at Wendy's new relationship.
"Sterling tried to remove all evidence of his presence from the scene by thoroughly cleaning the house but in his haste to leave left a plastic beaker with his DNA on the kitchen counter. His efforts to avoid suspicion almost worked.
"However, painstaking forensic examination and CCTV viewing placed Sterling at the scene at the time Wendy must have met her death. The jury upon listening to all of the evidence presented have reached the correct decision.
"We hope that today's verdict in some way brings closure to Wendy's family but recognise that painfully her children will grow up knowing that their father ended their mother life."
Wendy's brother Stephen Mann, speaking after the life sentence was passed down, added: "It has been a long process getting justice for Wendy.
"We are happy with the verdict today and hope that it will bring a sense of closure to our lives.
"The verdict will not bring Wendy back, but it gives us some comfort that someone has faced justice for this terrible act and her memory honoured.
"We would like to thank the police for all their efforts and support and hope that we can now move on with our lives."
Sterling was sentenced to life and will serve at least 21 years. He was also convicted of the attempted murder of a 53-year-old man and was jailed for six years which will run concurrently.
Following the hearing, senior crown prosecutor from West Midlands Crown Prosecution Service, David Parsons, said: "When Leroy Sterling became aware that Wendy Mann had formed a new relationship, jealously and rage took hold of him.
"He first brutally attacked the man she had formed the new relationship with and a month later he violently attacked and killed Ms Mann in her own home.
"Throughout this prosecution the defendant has shown no remorse for his crimes.
"He has today been found guilty and must now face the consequences of his actions.
"Our thoughts are with the family and friends of Ms Mann."