The 22-year-old Burundi international originally moved to the Magpies from the Sky Blues in July 2012 and also had a loan spell back at the Ricoh Arena last season.
Bigirimana made 25 appearances for United in all competitions during his four years on Tyneside but hasn’t featured for the first team since a League Cup tie at Morecambe in August 2013.
Everyone at Newcastle United wishes Gael all the best for his future at Coventry.