Devils executive vice president and general manager Ray Shero announced the deal Monday.
The 20-year-old Appleby attended training camp as an amateur tryout, after previously attending the team's development camp in July. He had spent the past three seasons with Oshawa (OHL), where he helped lead the Generals to the 2015 Ontario Hockey League and Memorial Cup Championships.
Last season, he led the league with a 2.08 goals-against average, .924 save percentage and six shutouts (tie). During the OHL playoffs, Appleby was 16-5 with two shutouts and a 2.24 GAA.