The 27-year-old joined Glasgow at the beginning of the season from Mosley.
But he and his family have struggled to settle in Scotland and he has signed a two-year contract to join Exeter Chiefs in the English Premiership.
"I've come up against Exeter in the past when I played for Mosley, so I know they are a very good team - that are not only skilful but also very physical," said Muldowney.
"Playing in the Magners League was obviously a step up in the standard I was used to in the Championship.
"I think I have added new things to my game during my time at Glasgow, but this a great opportunity to further my career."
"This was a very hard decision to make, but ultimately I have had to make the best decision for my family, who weren't settling in Glasgow I spoke to Sean Lineen, who understood this and was very supportive.
"So, when the offer came in from Exeter, it effectively killed two birds with one stone by moving my family close to relatives in Devon while offering me the chance to continue playing top-flight rugby."
During his time at the Firhill-based club, Muldowney has made 17 Magners League appearances and scored two tries.
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