Avery was cut by the Buccaneers on Tuesday, Rick Stroud of the Tampa Bay Times reports.
Avery initially signed with Tampa Bay on a one-year, $1.04 million deal last week after being dropped by Pittsburgh two days prior. The 27-year-old linebacker played 35 games over the past three seasons with the Eagles, and he will likely look to catch on in a reserve role with a new team this regular season.