The Coyotes also acquired Patrik Nemeth, a second-round pick in the 2025 NHL Draft and an optional pick in the 2024 or 2026 NHL Draft in a trade with the New York Rangers for Ty Emberson.
Bjugstad, a 29-year-old forward, received a one-year contract. He had 13 points (seven goals, six assists) in 57 games for the Minnesota Wild last season.
"For me it was just finding a spot where one team wanted me and I felt comfortable with within the depth chart," Bjugstad said. "Just judging off how they played the Wild]*
Selected by the Panthers in the first round (No. 19) of the 2010 NHL Draft, Bjugstad has 237 points (110 goals, 127 assists) in 540 regular-season games for the Wild, Pittsburgh Penguins and Panthers and five points (three goals, two assists) in 15 Stanley Cup Playoff games.
Brown, a 28-year-old defenseman, received a two-year contract. He had six assists in 52 games for the Ottawa Senators and Boston Bruins last season. Selected by Florida in the sixth round (No. 152) of the 2013 NHL Draft, Brown has 17 points (four goals, 13 assists) in 171 regular-season games for the Bruins, Senators and Panthers and no points in three playoff games.
"He is a big, strong, physical defenseman who will add experience and toughness to our blue line next season," Coyotes general manager Bill Armstrong said.
Stecher, a 28-year-old defenseman, got a one-year contract. He had three points (one goal, two assists) in 29 regular-season games for the Detroit Red Wings and Los Angeles Kings last season and four points (two goals, two assists) in four playoff games for Los Angeles after he was acquired from Detroit on March 20.
"I think the more he plays, the better he gets," Armstrong told the Coyotes website. "Tremendous amount of energy, grit, and hustle, and I'm looking forward to seeing him on our back end."
Nemeth, a 30-year-old defenseman, had seven points (two goals, five assists) in 63 regular-season games for the Rangers. He was held without a point in five playoff games. He has 65 points (10 goals, 55 assists) in 429 regular-season games for the Rangers, Colorado Avalanche and Dallas Stars and two points in 33 postseason games.
"I think we were trying to put some good, solid players in there that obviously would make us a very competitive, hardworking team," Armstrong said. "I think we accomplished that.
"We're in the same mode that we were last summer, trying to be as optional and build a team that gives us some options to take on some deals, move some people, and acquire some assets. At the same time, with our culture and everything, is be one of the hardest working teams in the National Hockey League."
Emberson is a 22-year-old defenseman who had 11 points (four goals, seven assists) in 58 games for Tucson of the American Hockey League last season.
NHL.com independent correspondent Jessi Pierce contributed to this report