The one-year deal is reportedly worth $900,000.
The 25-year-old unrestricted free agent was targeted by the Rangers in the wake of an injury to top defenseman Marc Staal. Staal has yet to play a game this season -- or practice -- because of headaches stemming from a concussion suffered last February.
Stralman attended training camp with the New Jersey Devils on a tryout but did not make the final roster. He skated with the Devils while unsigned before heading home to Sweden last month to take care of a visa issue. The Bergen (N.J.) Record first reported the Rangers interest last Monday.
Stralman spent the past two seasons with the Columbus Blue Jackets; he finished with one goal and 17 assists in 51 games last season.
Staal's injury left the Rangers in need of some depth on the blue line, a need that was then exacerbated when a preseason shoulder injury forced 24-year-old defenseman Michael Sauer to miss five games.
The team claimed Jeff Woywitka off waivers from Montreal one day before the official season began last month and currently have only six defensemen on their roster.
Twenty-year-old Tim Erixon was sent back to the team's minor league affiliate in Hartford, the Connecticut Whale, after playing the first nine games of the season.
Katie Strang covers the NHL for ESPNNewYork.com.