Aly Muldowney will leave Exeter Chiefs at the end of this season.
The Stafford-born second-row has been playing for the Chiefs for the last two years playing in five of their Heineken Cup games this season.
Muldowney, was signed from Glasgow Warriors, has agreed a three-year contract with the Galway-based outfit.
Commenting on the news, Baxter said: “Obviously we are sad to see Aly moving on from the club. He was offered a new deal by us, but obviously this move is a great opportunity for him and his family.
“We of course wish him all the best for the future and thank him for his contribution to the club. However, there is still just under half a season to go for us all and we envisage him playing his part between now and the end of the season.”
Muldowney,added: “It was a tough decision to leave the Chiefs because I have really enjoyed my time at the club.
“Since coming to Exeter I feel my game has come on leaps and bounds, especially working with Rob [Baxter], Ali [Hepher], Ricky [Pellow] and all the other coaches. Also the support I’ve received from everyone, especially the supporters, has been amazing.
“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.
“Having played against them before whilst at Glasgow I know that they are tough opponents, so I’m really looking forward to being a part of the team and adding what I can. It’s also an exciting time for the club also with a new Head Coach in Pat Lam coming in.”