The guilty verdicts returned against Aaron Wallace, Christopher Kerr and Jeff Lewis have been ruled unsafe, due to flaws in how the jury was directed.
The Public Prosecution Service must now decide by the end of the week if a retrial will be sought.
The 15-year-old victim, known as Micky-bo, was chased through the Co Antrim town in May 2006 before being caught and beaten with a baseball bat.
He managed to get home, but was taken to hospital and later from his injuries two days later.
Wallace, 23, formerly from Moat Road; Kerr, 25, from Carnduff Drive; and Lewis, 22, from Rossdale - all in Ballymena - were convicted of his murder and jailed for between 10 and 13 years.
A fourth man, 23-year-old Mervyn Wilson Moon from Douglas Terrace in the town, admitted the killing at the start of the trial.
Police will study the appeal decision and consult with the Public Prosecution Service and the McIlveen family about options for a way forward.
Lawyers for Wallace, Kerr and Lewis based their challenges on the guidance and directions the jury received during the trial judge's summing up.
They claimed there was a failure to expose the possibility that an eye witness may have been lying about the three men's alleged roles at the scene of the attack.
Kerr, who was the only defendant to give evidence at trial, accepted retrieving the murder weapon - a baseball bat - but denied using it.
He claimed he did not take part in the assault or encourage anyone else.
His barristers, Frank O'Donoghue QC and Sean Devine, argued that the trial judge failed to put a succinct, structured and impartial summary of his case to the jury.
They claimed the panel was wrongly invited not to rely on his evidence in any circumstances in the absence of supportive evidence.
Counsel for Lewis also contested the finding that he was guilty of murder as part of a joint enterprise.
Richard Weir QC argued that his client arrived at the scene separate from the others and knew nothing in advance about a baseball bat being acquired.
According to him, the fatal attack was mistakenly portrayed to the jury as having been planned and carried out by a cohesive, single-minded unit.
Wallace's legal team took issue with how bad character evidence against him was handled.
We grant the applications for leave to appeal and allow the appeals against conviction.
Lord Justice Higgins
Delivering judgment on the appeals, Lord Justice Higgins set out how the prosecution accepted inappropriate directions were given on some of the points.
"It was submitted that there were failings in the construction and sequence of the judge's summing up and in the choice of language used to express the opposing arguments raised in the trial," he said.
"Specifically, it was submitted that the evidence of the principal witness was not analysed in depth - in particular with reference to the contrary evidence of the expert pathologist in relation to his findings about the nature and number of injuries sustained by the deceased and found during the post-mortem examination."
Lord Justice Higgins, sitting with Lord Chief Justice Sir Declan Morgan and Lord Justice Coghlin, held that the cumulative effect of the points raised rendered all three men's convictions unsafe.
Following the verdict, Kerr clapped Wallace on the back before both men were returned to custody to await a decision on a possible retrial.
Lewis did not attend the three-day hearing due to illness.
Sir Declan confirmed that an eight-week slot beginning at the end of January was available if there is to be a fresh trial.
He added: "We would need to know by Friday what the Crown's position is."