The 29-year-old Irish international, who has agreed a two-year deal, is Baxter's fifth summer recruit so far having already added Thomas Waldrom, Moray Low, Mitch Lees and Tomas Francis to his playing roster for the 2014/15 season.
Caldwell's arrival in Devon will offer a welcome boost to his new coach, who this season alone has lost locks Tom Hayes and James Hanks to retirement and Romana Graham to French club side La Rochelle.
Baxter said: "People are aware that James Hanks had an injury, sustained against Bath, which meant he had to retire - and we also lost Tommy Hayes and Romana Graham so we had to look to strengthen our lock options. Mitch Lees can play in the second row if necessary, but we primarily see him as a bigger back-row option, so we have been quite strong in the market for locks.
"Right now we might be in the market for another because if you look at who we lost and how few we had available throughout the season, we are maybe one lock light. That said, I think Ryan is a really good signing for us. I have kept an eye on him ever since he came over because we were interested in signing him when he came over from Ulster, but we were never really in the market for him.
"Since then I have watched him over a number of seasons and when he first came over he played really well for Bath. He has had some injury issues, but they are behind him and he is fit and ready to play. We feel it's a great opportunity for Ryan to show what he can do."
As always Baxter has carried out a detail analysis of his new recruit - and he clearly enjoys what he sees from the 6ft 7in, 112kg forward.
"If you want to describe his style of play, he runs around, he likes to hit rucks, get his hands on the ball, make tackles and have a full involvement in the game," added Baxter. "That really suits us and how we play the game and we are looking forward to having him.
"His medical and physical testing went really well, he carried himself well, he was very self-aware of his game and I think he will definitely strengthen our back five and our scrum which now has some real quality about it. He is a guy who is always in the thick of the action and he is very sharp in the air too.
"Anybody who remembers the LV= Cup semi-final up at Bath, he turned over three or four of our line-outs cleanly by a leap quicker into the air. He works hard in the scrum too and likes to get himself involved in the game.
"I think if you look at our squad we are still relatively young. Ryan has had international experience and plenty of Premiership experience so that could be important for us. He also has plenty of miles on the clock though and he is raring to go."
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