The 28-year-old face of the Columbus franchise was sent to New York along with minor league defenseman Steven Delisle and a conditional third round draft pick in 2013 for forwards Artem Anisimov and Brandon Dubinsky, defensive prospect Tim Erixon and a first round draft pick in 2013.
Nash, the first-overall draft pick by Columbus in 2002, has scored at least 30 goals in seven of his nine NHL seasons and will be expected to spark a Rangers offense that had difficulty scoring in the 2012 NHL play-offs.
The transaction follows fives months after the Rangers failed to pull the trigger on a deal for Nash at the NHL trade deadline because the demands from Columbus were considered too high.
Nash, who shared the league-lead in goals when he scored a career-high 41 during the 2003-04 season, is a five-time NHL All-Star who has twice represented Canada at the Olympics and won a gold medal at the 2010 Vancouver Games.
He was widely expected to be dealt during the NHL's current off-season since the Blue Jackets had said in February that Nash had requested a trade.
Nash, who holds the Blue Jackets' franchise records for goals, assists and games played, had 30 goals and 29 assists last season on a Columbus team that finished last in the NHL.
The Rangers finished the 2011-12 regular season with the best record in the Eastern Conference but could average just 2.15 goals during the play-offs and lost in the third round.
Anisimov, a second-round pick by New York in 2006, had 36 points in 79 games last season while Dubinsky, a second-round pick by New York in 2004, had 34 points in 77 games.