Published Thursday, 29 May 2014
Constable Carroll was shot dead by the Continuity IRA in Craigavon in March 2009.
Three years later, Brendan McConville, 43, from Craigavon, and John Paul Wootton, 23, from Lurgan, were found guilty at Belfast Crown Court of murdering the 48-year-old officer from Banbridge, Co Down.
The appeal was heard in Belfast High Court last year by Northern Ireland's Lord Chief Justice Sir Declan Morgan, Lord Justice Coghlin and Lord Justice Higgins.
Their reserved judgment was delivered on Thursday.
McConville was sentenced to at least 25 years in prison for the murder. Wootton was handed a minimum 14-year term.
Outside the court, Stephen Carroll's widow Kate told UTV of her "relief".
She said: "It's been a long, arduous journey. I do feel sorry for Mr and Mrs McConville because I have a son of my own and I know what it's like to suffer, but I just want to move on from here."
Constable Carroll was shot dead in a dissident ambush two days after two British soldiers were murdered in a Real IRA gun attack outside their barracks in Antrim town.
He died of a single gunshot wound to the head sustained as he sat in an unmarked police car while colleagues attended a 999 call in the Lismore Manor area.
A brick had been thrown through the window of a house in the private development an hour earlier, prompting the occupants to call the police.
Constable Carroll was the first policeman killed by republican paramilitaries since the inception of the PSNI in 2001.
Following the ruling, Detective Chief Inspector Ricky Harkness again appealed for anyone with information about the murder to contact police.
He said: "Our thoughts today are with Kate Carroll and her family.
"The Police Service of Northern Ireland is committed to protecting communities and delivering a policing service through the criminal justice system.
"This case proceeded through the criminal justice system, passing every test in terms of grounds for arrest, evidence to charge, going to trial and securing convictions.
"The Court of Appeal has upheld those convictions."
He added: "We welcome this decision. It is an acknowledgement of all the hard work by Serious Crime Branch detectives and partner agencies to get justice for a valued and much missed colleague.
"More than two people were involved in the murder of Constable Carroll.
"Anyone with any information about others involved in the attack is asked to contact police on the non-emergency number 101. Information can also be provided anonymously to the independent charity Crimestoppers on 0800 555 111."
© UTV News