Henrique, who was traded by the New Jersey Devils with forward Joseph Blandisi and a third-round pick in the 2018 NHL Draft for defenseman Sami Vatanen and a conditional draft choice Nov. 30, 2017, had 36 points (20 goals, 16 assists) in 57 games with the Ducks.
Anaheim went 33-15-9 with Henrique last season.
"No matter where I would've been traded to, I feel like my game is complete enough to fit in anywhere," Henrique said. "But coming to Anaheim, and starting with all the injuries and getting to play a lot, it was a seamless fit. I don't think you can overlook that. I think that was a big reason why I was so comfortable there and playing well. The guys in the locker room were great to me.
"I felt like I had been there for years with some of those guys. That was important for me. Big reason why I wanted to stay and was so comfortable doing another five years. I'm excited it's done and excited for what's ahead. Looking forward to hopefully bringing a Cup back there."
Henrique has scored at least 20 goals in a season four times, including an NHL career-high 30 in 2015-16. He has 293 points (142 goals, 151 assists) in 512 NHL games with the Ducks and Devils.
Henrique was a third-round pick (No. 82) in the 2008 NHL Draft by New Jersey.