Matthew Scully-Hicks had gripped Elsie around the rib cage, shook her and may have banged her head against a hard surface.
He showed no emotion as the trial judge, Justice Nicola Davies, handed down the sentence.
An independent review is taking place that will consider whether social workers and health professionals missed chances to step in and protect Elsie before she was killed by Scully-Hicks, 31.
At least four social workers, a GP, a health visitor and hospital staff including a registrar saw or treated a series of injuries she suffered before the fatal attack.
The judge said Elsie’s fatal injuries were inflicted between meal time and bed time - a time when the infant was known to cry.
“It was Elsie’s behaviour, your frustration with it which turned to anger, which led you to inflict the serious injuries which swiftly led to her collapse,” Davies said. “The force which you used in gripping Elsie was sufficient to cause the fractures of the ribs, the shaking sufficient to cause severe brain and eye injury.
“In deliberately inflicting serious injuries upon your 18-month-old adoptive daughter you abused the trust which had been placed in you as Elsie’s adoptive father. It was a gross abuse of that trust.
“Your actions in killing Elsie have devastated three families – the birth family of Elsie, the family you had sought to build with Craig Scully-Hicks and your own birth family.
“You had, and were aware that you had, a predisposition to injure your adoptive daughter. You took no steps to prevent a recurrence of the earlier incidents when Elsie suffered injuries as a result of your actions,” the judge said, adding: “No remorse has been shown.”
Scully-Hicks described Elsie as “a psycho” in text messages, but the judge said he had not told his partner how much he was struggling.
The judge referred to the messages when she said: “In more than one text you describe Elsie as having a ‘diva strop’, you refer to Elsie in strong and derogatory language. The texts demonstrate your frustration at what you described as Elsie’s attitude, her crying and her strops.
“To those who saw you regularly, be it healthcare professionals, social workers or friends and family you were a loving and caring father. The difficult times were when you were alone with Elsie or with her and her adoptive sibling. You deny being unable to cope with two children, but the texts indicate otherwise.”
Scully-Hicks, who denied murder, gasped and wept as jurors at Cardiff crown court unanimously convicted him on their fourth day of deliberations.
The injuries suffered by Elsie before the murder included bruises to her forehead and a broken leg and she also fell down the stairs.