Rangers general manager Jeff Gorton announced the deal on Monday, one that included future draft picks.
The Rangers also will receive the Senators' second-round draft pick in 2018. Ottawa will get the Rangers' seventh-round pick that year.
The 28-year-old Brassard had a career-high 27 goals and finished second on the team with 58 points in 80 games last season. His 31 assists were 10 fewer than the previous season.
Zibanejad, 23, skated in 81 games with Ottawa with 21 goals and 30 assists. He established career highs in games played, goals, assists, points, game-winning goals (seven), and faceoff win rate (50.5 percent).