The franchise also signed long snapper Rick Lovato to a one-year deal through 2019. Financial terms of the deals weren't disclosed.
Elliott made 26-of-31 field goal attempts, including a franchise-record 61-yard kick against the New York Giants, as a rookie and had 117 points.
In the 2018 season, Elliott converted 26-of-31 attempts and had two game-winning kicks.
The Eagles originally signed Lovato late in the 2016 season. He has snapped in 37 career games over the last two years. He also has added seven special teams tackles.
Philadelphia also announced the release of safety Chris Maragos.