The 30-year-old, who played for Club Brugge, Valencia, Genk, Brighton & Hove Albion and Arsenal before his move to Sociedad, is keen to get as much game time as he can ahead of the World Cup in Qatar, which starts in November.
Australia captain Ryan, who has 73 caps, said in a statement he was looking forward to playing at Copenhangen, a club which has a "fantastic reputation throughout Europe."
"The team has great quality and the ambitions for the club are high in terms of winning titles and competing in the biggest tournaments in Europe," he said. "I will work hard to contribute to that."
Ryan made only nine appearances in all competitions last season and is set to replace Copenhagen's first-choice Kamil Grabara, who is sidelined with injury.
Copenhagen won their 14th Superliga title last season.