Dzingel, drafted by the Senators in the seventh round in 2011, had two goals and two assists in 11 games with the Hurricanes this season. He has 171 points (76 goals, 95 assists) in 343 career NHL games with Ottawa, Columbus and Carolina.
Galchenyuk, 27, scored one goal in eight games for the Senators, while Paquette, also 27, had one goal in nine games.
Galchenyuk has 321 points (136, 185) over 557 career games with five teams. Paquette has 86 points (48-38) in 386 career games with the Senators and Tampa Bay Lightning.
"Cedric is a strong, physical forward who won the Stanley Cup with Tampa Bay last season," Hurricanes general manager Don Waddell said in a release. "We're excited to add both of these players to our forward group."
Dzingel will have to quarantine for 14 days before he can play for Ottawa due to COVID-19 protocols.