According to Detroit Free Press reporter Helene St. James, who first broke the story via Twitter, the deal will be official at the end of the month, due to Philadelphia's salary cap restraints.
Cleary confirmed the news to St. James, telling her, "I'm going to Philly." His deal also includes a no-trade clause.
The 15-year NHL veteran registered nine goals and six assists for 15 points, along with 40 penalty minutes, in 48 games with the Wings last season.
Cleary, 34, has played in 869 career NHL regular-season games with the Chicago Blackhawks, Edmonton Oilers, Phoenix Coyotes and Red Wings, and has accumulated 160 goals and 217 assists for 377 points, along with 455 penalty minutes.
He was originally drafted 13th overall by Chicago in the 1997 NHL Entry Draft.