The 31-year-old forward had 44 points (25 goals, 19 assists) in 71 games with the Vegas Golden Knights last season. He scored the first goal in Golden Knights history and the winning goal in each of their first three games.
He had 11 points (six goals, five assists) in 20 Stanley Cup Playoff games last season, helping the expansion Golden Knights reach the Stanley Cup Final, which they lost to the Washington Capitals in five games.
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Neal also played with the Nashville Predators in the 2016 Final, won by the Pittsburgh Penguins in six games.
"For me, I want to win," Neal said. "I've been really close the last few years to winning a Stanley Cup. Once you get a taste you want more. We have great goaltending in [Mike Smith], and we have great guys up front and a good [defense] corps. I feel like we're really close to winning, and for me I hope I can be that little piece that they've been missing."
The Flames were 37-35-10 last season, 11 points behind the Colorado Avalanche for the second wild card into the playoffs from the Western Conference. Neal said he is confident that a foundation including forwards Johnny Gaudreau, who led Calgary with 84 points (24 goals, 60 assists), and Sean Monahan, who had a Flames-high 31 goals, will help Calgary reach the next level.
"I'm excited about those two guys for sure," Neal said. "That's definitely a big reason I wanted to come to Calgary. Those two guys are unbelievable players. They make everybody around them better. And like I said with the goaltending and D-corps, we're really close to winning. Hopefully I'm that piece that can push us over the edge and bring us a championship in Calgary."