Dallas acquired the forward from the Phoenix Coyotes in exchange for winger Mathias Tjarnqvist and a first-round draft pick. Nagy was one of the top names available ahead of the NHL's Feb. 27 trade deadline.
The 27-year-old has 41 points in 55 games this season.
He will be an unrestricted free agent this summer.
Tjarnqvist has four points in 18 games this year.