McNicholas has represented Ireland at the Under-18 level and becomes the sixth Irish member in the Wrexham roster alongside James McClean, Anthony Forde, Thomas O'Connor, Eoghan O'Connell and Liam McAlinden.
The 24-year-old said on the move: "I'm absolutely delighted. Since I’ve come over, I’ve really enjoyed it. It’s been a great group to come into, they’ve been really welcoming, and I’m really pleased to finally make my deal here a permanent one. I’m going to keep pushing in training, and to continue learning from the goalkeepers at the club to hopefully get my chance and the number one spot at some point in the future."