Cork-born Kelleher, a 6ft 5in centre-half, started his career at Celtic academy before permanent spells at Oxford United and Macclesfield Town before lionking up with Wrexham in time for the 2020-21 season.
On joining the club, Kelleher, who has also spent loan spells earlier in his career at Peterhead and Solihull Moors, said: “I am delighted to be here. It has happened quite quickly, but the gaffer was very positive on the project he wants to start here.
“Once he had told me all his players, I was desperate to come on board, and I just cannot wait to get going.
“I am a passionate player who is very competitive, will get stuck in and fight to the very last minute. I am vocal on and off the pitch and will look to do my job as well as I can.
“I want to bring consistency and am fully bought in to the plan in place. I want to help make sure we hit our goals and achieve our objective of promotion.”
Adams continued: “We are pleased to have Fiacre through the door as our seventh summer signing, as our squad ahead of next season continues to take shape.
“He is a strong character who, on the back of an impressive season at Wrexham, will add even more fierce competition to our defensive line.
“Fiacre is another player who adopts a win-at-all costs mentality, which will be essential if we are to be a successful side this season.
“His physicality and dominance in the air brings another dimension to our game, and we are looking forward to working with him over the next two years and beyond.”