The 28-year-old forward had 32 points (18 goals, 14 assists) in 71 regular-season games for the New York Rangers and Florida Panthers last season, including 13 points (eight goals, five assists) in 22 games after he was acquired in a trade by the Rangers on March 16.
Ryan Strome, Vatrano's teammate with the Rangers, signed a five-year contract with the Ducks.
"I think you can see all the pieces are there," Vatrano said. "There are great veterans on the team, guys who have been around a long time, and then you have younger guys who have proven themselves already at such a young age. When you have a good mix of veteran leadership and young players who can push the play, that's a sign of a great team."
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Vatrano had 13 points (five goals, eight assists) in 20 Stanley Cup Playoff games. He helped New York advance to the Eastern Conference Final, a six-game loss to the Tampa Bay Lightning while playing on the top line with Chris Kreider and Mika Zibanejad.
"Went to New York into an unbelievable situation, playing on the power play and playing in the top six," Vatrano said. "When the playoffs come around, you have to take your game to a whole new level and the regular season doesn't really mean much. It's just getting there and getting a chance to compete for the Stanley Cup. When you can produce and help your team out in the playoffs, it's extra special."
Signed by the Boston Bruins as an undrafted free agent March 13, 2015, Vatrano has 170 points (101 goals, 69 assists) in 401 regular-season games for the Rangers, Panthers and Bruins and 16 points (seven goals, nine assists) in 34 playoff games.
"Wherever this team sees me fit in the lineup, I'm going to do whatever it takes to play the best I can every single night," Vatrano said. "I'll bring the effort every single night. The future is very bright in Anaheim."