The deal could be worth up to $5.5 million, a source told ESPN NFL Insider Adam Schefter.
A standout at Texas, where he went 30-2 and led the Longhorns to a national championship only to have an up-and-down career with the Titans, Young will get a fresh start in Philadelphia, and won't have to deal with the pressure of performing right off the bat.
Released on Thursday after five years with the Titans, Young became the fourth Pro Bowl player to be acquired by the Eagles in two days, joining cornerbacks Dominique Rodgers-Cromartie and Nnamdi Asomugha, as well as defensive end Jason Babin.
Young, 28, won 30 of 47 starts with the Titans, but owner Bud Adams announced in January that the team planned to cut ties. His antics off the field, as much as his performance on it, probably cost him his job there.
After an overtime loss to the Redskins in November in Nashville, the Titans' third straight with Young under center, he threw his shoulder pads at booing fans and then had a postgame confrontation with coach Jeff Fisher.
He never played again.
With the Eagles, Young gets a fresh start and a chance to learn under coach Andy Reid and offensive coordinator Marty Mornhinweg, who, in just two years, helped re-energize Vick into an MVP candidate and Pro Bowl starter after his own troubled past.
"I'm looking forward to working with him," Vick said. "I think Vince will mature as a player. Get him in here and make him a better player.
"And if we ever need him, he's there for us."
Young finished second to Reggie Bush in the 2005 Heisman Trophy voting, when he led Texas to an 11-0 record, including that historic 41-38 win over previously undefeated USC in the BCS national title game. In the win, Young threw for 267 yards and ran for 200 more.
In five NFL seasons, Young has completed 58 percent of his passes with 42 touchdowns and as many interceptions. He's rushed for 1,380 yards, with a 5.2-yard average, and 12 more touchdowns.
The Eagles open the preseason on Aug. 11 vs. Baltimore at home. They'll open the regular season on Sept. 11, at St. Louis.
Information from The Associated Press was used in this report.