After losing longtime captain Daniel Alfredsson to the Detroit Red Wings, Ottawa picked up Ryan, a 26-year-old right-winger, by giving up Jakob Silfverberg, prospect Stefan Noesen and a first-round pick in 2014.
"Ottawa.... Im coming in hot," Ryan tweeted.
Ryan has been bandied about in trade rumours for more than a year. He had 11 goals and 19 assists last season with the Ducks.
He is a four-time 30 goal scorer and has 147 goals and 142 assists in 378 career games.
Alfredsson, 40, left Ottawa after 17 seasons to sign a one-year deal with the Red Wings.