Father-of-two Mr Black, 52, was gunned down as he drove to work at the high security Maghaberry prison in Co Antrim.
Police have blamed dissident republicans for the attack.
The men were arrested in the Lurgan area in Co Armagh.
Dissidents have been engaged in a long-running campaign against conditions in Maghaberry.
Mr Black was shot on a stretch of the motorway between Portadown and Lurgan.
A Toyota Camry used in the attack was later found burned out in the Inglewood area of Lurgan.
Mr Black, from Cookstown, Co Tyrone, had served in the Prison Service for more than 30 years and was considering retirement.
The long-standing member of the Orange Order became the 30th prison officer to be murdered in Northern Ireland since 1974, though the first for almost 20 years.
He was driving his black Audi A4 when the dark blue Toyota drew up alongside and several shots were fired.
His car immediately veered off the road and crashed into a drainage ditch though police believe he may have already been dead.
The arrested men have been taken to the Police Service of Northern Ireland’s serious crime suite in Antrim for questioning.