Anaheim announced the deal Tuesday. Terry will get $1.35 million in the 2020-21 season, $1.45 million in 2021-22 and $1.55 million in 2022-23.
The 22-year-old has eight goals and 20 assists in 81 career games with the Ducks, who drafted him in the fifth round in 2015. He scored 15 points in 47 games before the season was halted because of the coronavirus pandemic.
Terry has established himself in the NHL as an important part of the Ducks' young core, but the Denver native is best known for his shootout acumen at the international level.
The former University of Denver star scored the game-winning shootout goals in the semifinals and final of the 2017 World Junior Championship. He also played for the U.S. national team at the 2018 Pyeongchang Olympics, recording five assists in five games.
The Ducks are not participating in the NHL's return to play after posting one of the league's seven worst records. They have missed the playoffs in consecutive seasons for the first time since 2002. They will have the sixth overall pick in the upcoming draft.