The midfielder left Shamrock Rovers to emigrate to Canada where he will join the North American Soccer League outfit
Ryan, who previously played for Airtricity Premier Division outfit Shamrock Rovers, said that he was "delighted" to have been presented with the chance to play for the Canadian club and thanked club manager Marc Dos Santos for the opportunity.
"I am delighted to be given the opportunity by Marc who really impressed me when we spoke about joining Fury FC," Ryan told the club's official website.
"I've seen the project that the club and city are building and it is a privilege that Marc and John Pugh want me to be a part of what the club is building. I really believe that in the club's first season that we can bring success to the city."
Ottawa Fury boss Marc Dos Santos believes that the experience of the former Sligo Rovers and Dundee United midfielder will help the club progress.
"Richie is a player that will bring experience to our midfield," said Dos Santos.
"He has the exact profile we were looking for in a defensive midfielder. Richie is a winner and he will definitely push everyone around him."