The 26-year old defensive midfielder had impressed Peter Houston whilst on trial and the Scottish club were able to swoop ahead of Championship outfit Peterborough United to land the Sligo skipper.
Ryan joins the Tangerines on a free and was delighted to be making the move to the Scottish Premier League from the League of Ireland.
"I'm over the moon. It's nice to know my future is here at Tannadice for at least the next couple of years and I'm looking forward to getting started," he said.
"With the number of Irish lads already here, it will be a little bit easier to settle in.
"They've done well and I know I can bring something to the squad. I'm looking forward to joining up with my team-mates in December."