Casey's deal is worth $14.5 million, league sources told ESPN NFL Insider Adam Schefter.
A versatile player who also can line up in the backfield, the 6-foot-3 Casey has spent his entire four-year career with the Houston Texans.
Casey, 28, had 34 catches for 330 yards and three touchdowns -- all career highs -- last season with Houston. The 235-pounder has hauled in 66 career receptions in 61 games.
The Eagles already feature veteran tight end Brent Celek, who has been their primary starter for the past four seasons.
The moves were announced Tuesday night, hours after the Eagles released cornerback Nnamdi Asomugha on the first day of the NFL free agency period.
Chung, formerly with New England, and Sopoaga, formerly with San Francisco, also got three-year deals. Fletcher, formerly with St. Louis, and Phillips, formerly with Carolina, got two-year contracts.
The Eagles' busy offseason will continue Wednesday, as San Francisco 49ers free agent defensive lineman Ricky Jean-Francois will visit Philadelphia, league sources said.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.