Tate's contract situation - and his impending free agency - had loomed over this entire season, with reports surfacing as far back as training camp that other teams were calling about his availability.
Tate wrote on Twitter: "It's been real DETROIT!".
Tate, 30, has 44 catches for 517 yards and three touchdowns this season. I'll love ya forever.
He went to the Pro Bowl after the 2014 season after spending his first four seasons with the Seahawks.
He may be just a half-season rental for the Eagles, who are now a disappointing 4-4 and in second place in the NFC East behind Washington. Philadelphia will host the division rival Dallas Cowboys in a primetime game on Sunday, November 11 when they return from the bye week.
Coming off a win against the Jacksonville Jaguars in London on Sunday, the Eagles, 4-4, are sitting in second place in the NFC East behind the Washington Redskins.