The former Liverpool frontman has completed his move having flown out to Ireland to sign the deal which sees his time with the Shaymen come to an end.
Morgan joined FC Halifax in December 2016 on an eighteen-month deal signing from National League North side Curzon Ashton.
He has started a dozen times for Town this season, scoring 4 goals, and his last appearance was as a late substitute against Macclesfield Town at the MBi Shay Stadium on New Year's Day.