The Senators bought out Ryan's deal last month. He had two years left on his contract at a $7.25 million cap hit and was owed $15 million in real cash.
Ryan won the Masterton Trophy, the NHL's award for perseverance, on Sept. 7 after publicly sharing how he has addressed his risky use of alcohol. He entered the NHL/NHLPA players assistance program on Nov. 20 to get help with his addiction.
A long conversation with Detroit general manager Steve Yzerman sealed the deal even though it was the first discussion Ryan had with suitors during NHL free agency.
"It was a 45-minute call that left me with the feeling that it was the right fit without knowing else what else was out there,'' Ryan said Friday.
A four-time 30-goal scorer earlier in his career, the 33-year-old has struggled in recent years. Ryan had 15 goals and 42 points in 2018-19 and eight points in 24 games this past season.
The Wings also inked defenseman Jon Merrill to a one-year, $925,000 deal. He skated with Vegas last season and had seven points in 49 games.
Information from The Associated Press was used in this report.