Staal, 35, is a three-time 40-goal scorer who had one season remaining on his deal with the Wild. He was scheduled to make $3-million this coming winter. He turns 36 next month.
Staal's 42 goals in 2017-18 tied Marian Gaborik's Wild franchise record for goals in a season.
Staal is sixth among active players with 436 goals and eighth with 1,021 points.
Johansson turns 30 next month. He's played 10 seasons in the NHL with Washington, New Jersey, Boston and Buffalo.
He scored 9 goals, 21 assists in 60 games with Buffalo this past season and is due $4-million in salary this coming season.
Johansson has 102 goals in 501 career NHL games. His 24 goals in 2016-17 in Washington were a career high.
The Capitals drafted Johansson with the 24th overall pick (1st round) in the 2009 NHL Draft.