Sky Blues manager Chris Coleman said: "We have acquired not only a very good technical footballer but also a very tenacious and hard-working one.
"He [Deegan] will complement the players we already have here."
Deegan scored five goals in 34 appearances for Bohemians and has Champions League experience.
The playmaker had reportedly attracted interest from Premier League clubs.
Coleman added: "There were a number of other clubs interested in Gary's services so it was important we moved quickly.
"I'm very much looking forward to working with him when he becomes eligible for us in the New Year."