Nygren, 22, won the Salming Trophy as the top defenceman in the Swedish league this season. He led the circuit's rearguards with 13 goals and was fourth in points with 32 for the Farjestad club.
The six-foot-one 191-pound Nygren, who signed a two-year contract, was drafted 113th overall by Montreal in 2011.
Collberg, 19, signed a three-year deal. The five-foot-11 181-pound right winger had six goals and three assists in 35 games for Frolunda this season. He completed the season by playing two games with AHL Hamilton.
He also helped Sweden to a silver medal at the world junior championship with four goals and two assists in six games.
He was drafted 33rd overall in 2012.