Wheaton, who was initially signed by the Eagles to a one-year contract on May, was released by the team as it trimmed its roster to 53 over the weekend.
The addition of Wheaton comes after coach Doug Pederson ruled out wide receivers Alshon Jeffery (shoulder) and Mack Hollins (groin) for the Eagles' season-opening game on Thursday against the visiting Atlanta Falcons.
Wheaton missed Philadelphia's first three preseason games with a hamstring injury. He played in 16 snaps during the final preseason contest but did not record a catch.
The 27-year-old Wheaton collected just three receptions for 51 yards in 11 games last season with the Chicago Bears, with whom he signed a two-year, $11 million contract.
Wheaton has 110 catches for 1,559 yards with eight touchdowns in five seasons since being selected in the third round by Pittsburgh in the 2013 NFL Draft.
Jeffery was bothered by the shoulder injury last season, but still had 57 catches for 789 yards and nine touchdowns in the regular season. He added 12 receptions for 219 yards and three touchdowns in the Eagles' three postseason games en route to winning the Super Bowl.
Rodgers would be eligible to return after eight weeks if he's deemed healthy. He is in line to be the third tight end behind Zach Ertz and rookie Dallas Goedert.
The 26-year-old Rodgers signe a one-year deal with the Eagles in the offseason.
Rodgers is coming off his worst season with the Green Bay Packers. He started only one of 15 games and had a career-low 12 receptions for 160 yards and a touchdown.
The 6-foot-4, 257-pound Rodgers had his best season in 2015, appearing in all 16 games and making 12 starts. He finished with career highs across the board -- 58 receptions for 510 yards and eight touchdowns.