The 29-year-old has made 35 appearances in two seasons for the Chiefs following a move from Glasgow Warriors.
"It was a tough decision to leave the Chiefs because I have really enjoyed my time at the club," Muldowney told Exeter's official website.
"Moving to Connacht, though, is a great opportunity for me and my family. I have watched them play in the Heineken Cup this year and they are a really tough side with some great players."
Exeter are currently in seventh place in the Aviva Premiership table.