Financial terms were not disclosed.
Dziurzynski, 24, had 13 goals, 25 points and 91 penalty minutes in 68 games last season with the Binghamton Senators, Ottawa's American Hockey League affiliate.
He last played in the NHL in 2012-13, scoring two goals in 12 games.
Johnson, 31, had four goals and 40 points last season playing for the Hartford Wolf Pack, the Rangers' AHL affiliate. He has 17 goals and 62 points in 291 NHL games for the Boston Bruins, Calgary Flames, Chicago Blackhawks, Columbus Blue Jackets, Edmonton Oilers and New York Islanders.