Howard, originally from Co Laois, was charged with the murder of Arlene Arkinson in 2002, but acquitted in 2005.
He died in prison custody in England in 2015 while serving a life sentence for the rape and murder of 14-year-old Hannah Williams from London.
Ms Arkinson's body has never been found, despite extensive searches.
Following a long-running inquest, coroner Brian Sherrard, at Omagh courthouse, found that she died on the morning of Sunday August 14, 1994.
"There is no record of her being alive after that date," he said.
"Robert Howard, a violent sexual offender, and the last person to be seen with Arlene in the early hours of August 14, 1994, was responsible for her death.
"The mechanism of death is unknown.
"The court is confident of the date of death as Howard began establishing an alibi from the morning of August 14, 1994 at a time when Arlene's disappearance had not become known."
The coroner also ruled that the death happened in Northern Ireland but the precise location remains unknown.
"However the court is confident that Arlene's remains were secreted in this jurisdiction," he said, adding that Howard was familiar with the Castlederg area and the nearby Irish border was then actively patrolled by the security forces.
"The time available before sunrise was very limited indeed," he said.
The coroner noted "quasi admissions" by Howard, such as his inquiries to a number of police officers about serving his sentence in Northern Ireland if he admitted to certain things, needing help but being afraid to take the next step, living in fear, crossing the road when he saw a police officer, being haunted and seeing a face in a crowd and being reminded of the girl.
He said they "fell short of a confession but indicate culpability".
Reacting to the coroner's ruling, Ms Arkinson's sister Kathleen said there was now no doubt Robert Howard murdered her.
Ms Arkinson, who also alleged that that Howard had been working as a state agent, called for a public inquiry into his activities in Northern Ireland.
"This was a 14-year-old inquest, nearly as long as Arlene's life," she said.
"An inquest that Howard and the state never wanted. It was opened in November 2007 and only finishes today.
"Twenty-seven years on from Arlene's murder, I am still searching for her body. What else can I do? What else would anyone expect me to do? Despite what has happened, I have placed my faith in our justice system and went with it.
"Therefore I appeal to the Justice Minister (Naomi Long) to examine Arlene's case carefully.
"When she does, she will see that the need for a public inquiry into the activities of Robert Howard in this jurisdiction and his status as an agent for the RUC, which has led to death and misery for many people, will be unavoidable.
"I guarantee the minister that the more she looks into Arlene's case, the more outraged and terrified she will be on behalf of the public. But, above all, I want a Christian burial for my sister. In seeking the truth, through public inquiry, maybe I will achieve that."
Ms Arkinson, 15, was last seen alive on Sunday August 14, 1994 in a car with Howard.
The St Eugene's High School student, whose mother had died in 1990, was noted as being known to social services, but the coroner paid tribute to the commitment by her six older siblings to her welfare as "truly remarkable".
The coroner dismissed several rumours from the time of Ms Arkinson's disappearance, including that she had left Castlederg voluntarily, that she had been suicidal or had been pregnant.
He also dispelled any suggestion that members of Ms Arkinson's family had been involved in her murder.
The inquest, which has been running for more than a decade, was described as having "re-energised" police investigations on both sides of the border.
Mr Sherrard noted it had been 27 years since Arlene went missing.
He said the findings of the inquest had originally been scheduled to be delivered in March 2020, but were delayed due to the Covid-19 pandemic and other issues.
Concluding his findings, he said: "I would like to reflect on Arlene, who would now be a woman in her 40s, and it is a matter of profound regret that Arlene did not get to live her life and to live to her full potential.
"And I would also like to reflect on the very grave injustice that has been done ultimately to the Arkinson family due to the actions of Robert Howard, and I would like to reflect on the exhaustive manner in which Kathleen (Arlene's sister) in particular has driven this case from the first days after the disappearance right through to today, and that is remarkable and Arlene herself has been served exceptionally well by her family in the intervening 27 years."