Farrelly, 28, has signed until the end of the season after his contract at Bolton Wanderers was terminated.
He has spent spells at Bradford and Burnley this season on loan and has played at the JJB for Bradford. He will wear squad number 15.
To date the Irishman has started 137 games during his professional career.
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The official site has also commented about the rearrangement of the Gillingham ficture, it reads: "Meanwhile, Latics are disappointed to confirm that their away game at Gillingham will now be played on Tuesday 6th April. The new date is disappointing as the club were hoping to avoid playing then, as it means that supporters now have the two longest away trips of the season within three days of each other (Latics are away at Norwich on Friday 9th April).
Latics snap up Farrelly on free transfer
However, it has been decided that this is the date that the game must be played and though the club made their feelings known about this date being less than ideal, it has now been confirmed that the game must go ahead then."