Rangers general manager Jeff Gorton announced the deal, which included draft picks, on Monday.
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.
"I was a little shocked when it happened today,'' Brassard said Monday. "But I'm really happy to be joining the Sens and playing at home. I really like their team. I really like the balance of their team all the way from the goaltender all the way out to the forwards. I think they're the up-and-coming team and with Guy Boucher being the coach, I think it's going to be really good for the team.''
Zibanejad said Tuesday he was just as stunned after learning the Senators were dealing him to New York.
"This trade wasn't really on the radar for me, at least I didn't hear anything about this,'' Zibanejad said on a conference call. "It came as a shock and surprise, but like I said before I'm happy for it right now, obviously, and I'm really excited to kick off the season there.''
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). He has scored at least 20 goals in each of the past two seasons.
"I think the potential is there for more upside,'' Gorton said Monday of Zibanejad. "He is just scratching the surface at age 23. There are not a lot of guys who have done what he has done as far as scored 20 before that age.''
Zibanejad gives New York a player who has had success in the shootout. He has tallied a goal on 13 of his 28 career NHL shootout attempts, and he has five game-deciding goals in the shootout.
Zibanejad led the Senators in game-winning goals, faceoff wins and faceoffs taken, ranked third in short-handed goals (two), tied for third in games played, tied for fourth in assists, and ranked fifth in points and power-play points (11) in 2015-16. He also ranked third among Ottawa forwards in short-handed ice time per game (1:25).
The 6-foot-2 Swede has skated in 281 NHL games over parts of five seasons (2011-12 to 2015-16), getting 64 goals and 87 assists. He was selected by Ottawa with the sixth overall pick in the 2011 draft.
Brassard skated in 254 games with the Rangers over parts of four seasons, getting 69 goals and 105 assists. He was acquired by New York from Columbus in April 2013 in a multiplayer trade that sent forward Marian Gaborik to the Blue Jackets.
Zibanejad will be a restricted free agent after the 2016-17 season and will earn $2.62 million.
Brassard is under contract through 2018-19, earning $5 million annually.
"Our ultimate goal is to make the playoffs again, and we feel that Derick's going to help us make the playoffs,'' Senators general manager Pierre Dorion said Monday. "There's also more: We feel that Derick provides great talent, brings leadership into our room. He's someone that's played a lot of games in the NHL more than Mika.''
The Associated Press contributed to this report.