Devils general manager Lou Lamoriello did not disclose any contract terms in making the announcement. Most of the players will play in the minor leagues this season.
Also signed were defenseman Peter Harrold and nine other forwards -- Matt Anderson, Bryan Haczyk, Brad Mills, Nathan Perkovich, Tim Sestito, Myles Stoesz, Joseph Whitney, Chad Wiseman and Steve Zalewski.
Haczyk, Perkovich, Stoesz and Whitney were signed to AHL contracts.
Of the group only Sestito and Mills saw NHL action with the Devils last season. Sestito had two assists in 36 games, while Mills had a goal in four games.
Clermont, 19, spent each of the past four seasons with Gatineau (QMJHL), compiling a 90-60-11 mark in 185 appearances. The Devils drafted the Montreal native in the sixth round last year.
The 29-year-old Veilleux split the 2010-11 season with teams in Finland and Switzerland. He had 46 goals and 53 assists in 438 NHL games with Minnesota and Tampa Bay.
Harrold, 28, spent each of the past five seasons with the Kings' organization, scoring eight goals in 164 NHL games. Anderson led the Devils' AHL team in Albany last season with 32 assists and 55 points. And Haczyk spent 2007-11 with Niagara (CHA/AH).
Perkovich had eight goals and nine assists in 40 games with Albany last season. And Stoesz split each of the last two seasons between the ECHL and AHL Devils.
Whitney spent the past four seasons at Boston College, where he had 40 goals and 102 assists in 161 games played for the Eagles, a Division I powerhouse.
And Wiseman had 16 goals and 28 assists in 48 games with Albany, while Zalewski, also with Albany, had 11 goals and 12 assists in 31 appearances.