The deal is worth $36 million, with $26 million of that guaranteed, according to ESPN's Adam Schefter.
In Philadelphia, Bradford started 14 games. He missed two games after spraining a shoulder and receiving a concussion in a game against the Miami Dolphins.
Before the injury, Bradford and the Eagles offense struggled through the early part of the season. The offensive line was not cohesive, causing running back DeMarco Murray to be ineffective while Bradford threw 11 touchdowns and 10 interceptions. He said later that it took a few weeks to regain confidence in his surgically repaired knee.
In his five games after returning from the injuries, Bradford completed 65 percent of his passes. He threw eight touchdown passes and four interceptions, with a passer rating of 93.2.
New Eagles head coach Doug Pederson said in his introductory press conference that Bradford was a "perfect fit" for the offense Pederson plans to run.
Bradford was the first overall pick in the 2010 NFL draft. He was the offensive rookie of the year after completing a rookie-record 354 passes for 3,512 yards, the second most ever by a rookie.
But injuries have been a problem for the former Oklahoma quarterback. He started only 10 games because of injuries, including a high ankle sprain, in 2011.
The most recent season in which Bradford played all 16 games was in 2012, but he tore the ACL in his left knee seven games into the 2013 season. The next summer, Bradford tore the left ACL again in a preseason game. He missed the entire 2014 season. The Rams decided to move on after paying Bradford $65 million over five years for 49 games and an 18-30-1 record.
ESPN Eagles reporter Phil Sheridan contributed to this report.