The versatile 19-year-old passed a medical on deadline day and has penned a contract that will keep him at Portman Road until the summer of 2021.
Cotter becomes the second player to be signed by Ipswich from the League of Ireland during the January transfer window, with Aaron Drinan joining from Waterford United.
"I can't wait to get going now. It's a fantastic opportunity for me to learn here," Cotter told the official Ipswich website.
"It's a big step up for me but I'm confident it's one I can make. I've not set myself too many goals yet. I'd like to break into the first team obviously but for now, I just want to get my head down and work hard and show people what I can do.
"With the manager and coaching staff here I feel I can really improve as a player and that's my main aim for now."
Cotter, who can play right-back, in the middle of the defence or in midfield, has been capped by the Republic of Ireland at Under-19 level.