Kenny Richey is due to return to the UK following his release from prison in the US.
Richey reached a plea deal with prosecutors over an arson attack in which a two-year-old girl died in Putnam County, Ohio, in 1986.
He thanked those who "never doubted" him and said he was looking forward to "going home to Scotland".
The 43-year-old, who was brought up in Edinburgh, is expected to arrive in the city on Wednesday.
After spending the night at the home of his brother Steven, Richey is expected to leave Dayton, Ohio, on Tuesday afternoon on a flight to Chicago before flying first to Heathrow, London, and then on to Edinburgh on Wednesday afternoon.
He was convicted in 1987 of an arson attack on an apartment block in which Cynthia Collins, two, died but the sentence was overturned in August last year.
On Monday, he pleaded no contest to charges of attempted involuntary manslaughter, child endangering and breaking and entering at the Putnam County Common Pleas Court in Ottawa, Ohio.
He was sentenced to a total of 21 years - time which he has already served, most of it on death row.
On his release from the Putnam County jail Richey told reporters: "It's been a long time coming."
He faced an angry reaction in court to his plea deal from relatives of Cynthia Collins, who told him to "burn in hell".
In a statement read at the hearing, Cynthia's father, Robert Collins, said: "I just wish Cynthia could appeal her death and come back to life."
Karen Torley, Richey's former fiancée and long-time campaigner for his release, said he faced tough challenges coping with life in Scotland after 21 years in prison.
The family of Cynthia Collins hit out at Richey's release
Ms Torley said: "He's going to find it hard to cope I think, to adjust to all the different things.
"He's been in prison half of his life and now he's going to come home and try to make choices and try to live a normal life and I think he's going to find that really hard once the excitement of being free is over."
Richey left his mother's home in Edinburgh at 18 to live with his American father in Ohio.
On his return to the UK, PR guru Max Clifford will represent the former convict.
Mr Clifford dismissed criticism that Richey should not be able to profit from his time in prison.
He said: "It's the kind of money that will hopefully tide him over the first year of freedom because he's not getting millions of pounds of compensation for the 21 years he's been locked up.
"This is the only chance he's got of making some money."