Mr Holmes posted on Facebook: "Got out of jail peeps, thanks for the support."
IS controls large swathes of territory in Syria and north and west Iraq.
Mr Holmes`s mother met Kurdish officials on Friday to help secure his release.
The three men were held for more than a week in a prison in the Kurdish city, Erbil.
Shortly after his release, Mr Holmes told the BBC: "It feels good to finally be out, hopefully no more trouble and we`ll be on the way home soon."
Mr Ackerman updated his status on Facebook with a single word: "Free".
A Foreign Office spokeswoman said: "We are helping two British men make arrangements to leave [Iraqi] Kurdistan after they were released from custody."
Confirming the release of Mr Molloy, a former Royal Irish Regiment soldier, Ireland`s Foreign Affairs Minister Charlie Flanagan said: "I welcome Joshua`s release and I am pleased that he is now on his way home to join his family in Ireland."
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