Prosecutors in the US have said they are "disappointed" by the decision to quash the conviction of Kenny Richey.
Kenny Richey has spent 18 years on Death Row in Ohio
Ohio state prosecutors have 90 days in which to seek a retrial of Richey, 40, from Edinburgh, for the murder of two-year-old Cynthia Collins.
It follows a judgment by the 6th US Circuit Court of Appeals which ruled that the original trial was flawed.
Kim Norris, spokeswoman for the state Attorney General's Office, said: "We are disappointed in the ruling."
Mr Richey has spent 18 years on Death Row and once came within an hour of being executed by electric chair before winning a reprieve.
In a statement, Ms Norris said four separate courts had found that there was sufficient evidence to convict Richey of the "terrible crime".
She said: "A three-judge panel, the Ohio Court of Appeals, Ohio Supreme Court and Federal District Court, all agree the evidence against Ken Richey proved his guilt in committing this terrible crime that killed two-year old Cynthia Collins.
"At least three people heard Ken Richey threaten to burn down the building.
"Richey admitted to one person after the fire that he set it, saying, 'Looks like I done a helluva a good job, don't it?'.
"Ohio law allowed for the death penalty based on these facts. Our office is consulting with the Putnam County Prosecutor's office."
In the latest ruling, appeal court judges said there had been flaws in the original trial, in which he was found guilty of starting a fire at the toddler's mother's apartment in the town of Columbus Grove in 1986.
State attorneys have 90 days in which to decide whether to ask the full circuit court or the US Supreme Court to consider the case. If not, Richey will be freed.
Jeff Gamzo, from the American Civil Liberties Union, said an appeal was certain because "Ohio does not just say 'okay, we've lost, let it go'".
Mr Gamzo told BBC Radio's Good Morning Scotland programme: "This is step one. This is the first victory.
The appeal court's 26-page ruling which quashed the conviction
"They [the state of Ohio] are going to appeal. They officially have not decided that yet but in fact they will.
"They will ask either this court to rehear it or they will ask the United States Supreme Court to hear the case and there is no telling what will happen.
"Courts are unpredictable and Kenny has not been obviously successful in the courts up until today."
Other legal experts have suggested that a retrial is highly unlikely because some of the witnesses at the trial have died and others have been discredited.
Campaigners and politicians around the world have pressed for Mr Richey's freedom since he was convicted.
Thursday 27 January marks 18 years to the day since he was put on Death Row.
Before Tuesday's judgment was handed down, supporters had organised a vigil outside the US Consulate in Edinburgh.
Mr Richey was convicted of killing Cynthia Collins
Richey's mother Eileen, who lives in Edinburgh, said she wondered if her ordeal would soon be over.
She said: "Many a time I've given up hope, I never thought I would really see him again, but you've just got to get on with life, there's nothing else you can do."
But Jim Beutler, who was one of the first fire fighters on the scene in 1986, said he could not believe the decision to overturn the conviction.
Mr Beutler, who is now the local sheriff, said: "I was somewhat surprised to hear the ruling, especially after all the appeals the case has been through over the last 18 years, and unfortunately the higher court has made a decision here to overturn everything."
BBC reporter in Washington Michael Buchanan said that the sense he was getting from people he had spoken to in Ohio was that the state would appeal.
He said: "Locals are saying that this case is not about Kenny Richey, this case is about Cynthia Collins, the two-year-old girl who died in the fire in 1986.
"A lot of people frankly believe that Kenny Richey is guilty, many people believed this case had been done and dusted and they still can't believe that it's going through the courts system.
"If prosecutors go to the local appeals court, the US Supreme Court, some people are saying that could take about a year or so.
"A new trial could be somewhere in the region of a year away, so the sense in Ohio is that Kenny Richey will not be freed any time soon."
Meanwhile, it has emerged that Kenny Richey's brother could also be released from prison in the US.
Tom Richey is serving a 65-year sentence for shooting dead a shop assistant while high on drugs.
He has written to independent MSP Margo MacDonald saying sentencing reforms mean he could be released in August.