The Columbus Blue Jackets on Monday dealt the winger back to Philadelphia, where Umberger spent the first three seasons of his NHL career.
The Flyers also acquire a 2015 fourth-round draft pick while the Blue Jackets receive left-winger Scott Hartnell, who joins his third team after beginning his NHL career in Nashville.
Umberger, 32, had 18 goals and 34 points in 74 regular-season games this past season for the Blue Jackets.
He recorded 120 goals and 250 points in 445 games over six seasons for the Blue Jackets.
In 228 contests for the Flyers, Umberger had 49 goals and 116 points.
He helped Philadelphia reach the Eastern Conference final in 2008, posting 10 goals and 15 points in 17 games.
Hartnell, also 32, had 20 goals and 52 points in 2013-14.
He spent seven seasons in Philadelphia, totalling 157 goals and 326 points in 517 regular-season games.
The trade is the fifth in the past three years between the teams.