Neighbours heard the former lifeguard shouting "shut the f--- up" at Elsie and calling her a "little f------ brat" when she cried.
Scully-Hicks insisted he never harmed Elsie and claimed she must have spontaneously suffered fatal injuries after he changed her for bed at home in Llandaff, Cardiff, on May 25 last year.
But following the trial lasting more than four weeks, during which 12 medical experts and six doctors gave evidence, jurors unanimously found him guilty of murder. The jury returned their verdict on their fourth day of deliberating the case.
An independent Child Practice Review is now under way to examine the "tragic circumstances" of Elsie's death, a spokesman for Cardiff and Vale of Glamorgan Regional Safeguarding Children Board said.
Following the verdict, prosecutor Paul Lewis QC told the court: "Elsie was particularly vulnerable by reason of her age.
"There was a gross abuse of trust on the part of the defendant. We invite the court to bear in mind the nature and the extent of the injuries suffered.
"All the injuries suffered by Elsie in her short life while living with the defendant were deliberately inflicted by him."
The court heard Elsie was fit and healthy before she was murdered by her adopted father on May 25 2016.
She attended a toddler gym class, played on swings at a local park and accompanied her father shopping.
During his evidence, Scully-Hicks told the jury they had bought an outfit for Elsie to wear at a party to celebrate her adoption.
After finishing her dinner, at about 5.45pm, she walked "hand in hand" with Scully-Hicks into the lounge and was changed for bed, the defendant said.
In a 999 call at 6.18pm, he told the operator: "I was just changing my daughter for bed and she went all floppy and limp."
Mr Lewis said: "We submit this must have been [an attack] that required considerable force in gripping of the child because of the medical evidence of the fractures of the wrist. There must have been forceful shaking.
"There must have been gripping and shaking. Either her head was hit against a hard surface, or a hard object was used to strike Elsie to the head."
In police interviews and during his evidence, Scully-Hicks said he had left Elsie alone for a few minutes before returning to find her unresponsive.
Police and paramedics arrived at the property at 6.26pm and found Elsie not breathing, with no pulse, in the lounge.
Tests later revealed she had suffered three separate areas of bleeding on her brain, retinal bleeding, a skull fracture and three rib fractures. Elsie died in hospital in the early hours of May 29.
Scully-Hicks left full-time work to care for Elsie, who was placed with the couple in September 2015, while his husband worked.
Mr Lewis said the toddler did not "co-operate" with the routine the couple wanted to put in place and was difficult at meals and bedtime.
Elsie fractured her right leg in two places in November 2015 and suffered bruises to her head in December, and January 2016.
In March, Elsie was taken to hospital after apparently falling down the stairs. All of Elsie's injuries allegedly took place when she was alone with Scully-Hicks, who was nicknamed "safety boy" by his husband.
Scully-Hicks claimed that medical evidence that could explain his daughter's injuries had not yet been found.
A vitamin D deficiency may have left Elsie's legs more susceptible to fractures, his barrister told the court.
Representing Scully-Hicks, Robert O'Sullivan QC said his client had been examined by two psychiatric experts.
"Matthew Scully-Hicks doesn't suffer from any psychiatric illness or personality disorder," Mr O'Sullivan said.
Scully-Hicks has no previous convictions and is of previous good character, he added.
"It is consistent with the jury's verdict, and the evidence heard was this offence was committed in a sudden and unpremeditated outburst of frustration," O'Sullivan told the court.
"There is no evidence that he had any animosity to Elsie that day."
Scully-Hicks will be sentenced at 2pm on Tuesday.
