In exchange for the five-time all-star and team captain, the NHL-worst Blue Jackets received forwards Brandon Dubinsky and Artem Anisimov, defensemen Tim Erixon and Steven Delisle, a 2013 first-round draft pick and a conditional third-round selection.
The conditional pick will be returned to the Rangers should they make the Stanley Cup Finals in the 2012-13 season.
Nash, 28, spent all nine years of his NHL career with Columbus, where he has racked up 289 goals and 547 points, including seven seasons of 30-or-more goals.
The Toronto-area native played in all 82 games for the last-place Blue Jackets last season, amassing 30 goals and 59 points.
Dubinsky, a six-year veteran, managed only 10 goals and 34 points over 77 games for the Rangers last season, while Anisimov compiled 16 goals and 20 assists through 79 contests.
Rookie Erixon notched a pair of assists in 18 games for New York last season.