General manager Lou Lamoriello confirmed the signings to The Record on Thursday.
Corrente's deal is said to be a one-year, two-way contract worth $525,000 at the NHL level or $105,000 at the AHL level.
The 24-year-old played 39 games last season for Albany of the American Hockey League. He had two goals, six assists and 73 penalty minutes.
A first-round pick (No. 30) by the Devils in 2006, Corrente has 34 games of NHL experience.
Carrier and DeSimone were signed to AHL contracts, the report says.
Carrier, 21, played last season in Austria.
DeSimone, 25, had 14 goals and 19 assists with Hamilton, Montreal’s AHL affiliate, last season.
Lamoriello also confirmed the Devils earlier re-signed defenseman Mark Fayne.
Fayne, who is recovering from offseason wrist surgery, said he will be ready for the season opener in October.