The 28-year-old Syvret had six goals and 34 assists in 76 games last season with Adirondack of the AHL. He led the Phantoms with 34 assists, was second in points, and was third with five power-play goals. His 194 shots on goal were tops on the team.
In 59 career NHL games with Edmonton and Philadelphia, he has three goals and four assists.
New York, which was in need of defensive depth and help on the power play, has acquired two defensemen in two days. The Rangers obtained Justin Falk from Minnesota on Sunday before the NHL draft.
The 31-year-old Newbury split last season between the Rangers and Connecticut of the AHL.