The 30-year-old Hjalmarsson had spent his entire 10-year career with Chicago, helping the Blackhawks to three Stanley Cup titles. The Swede had five goals, 13 assists and a team-high 181 blocked shots in 73 games last season.
"We are very pleased to acquire Niklas," Coyotes GM John Chayka said in a statement. "He’s an elite player and one of the NHL’s top defenceman. He’s a warrior who played a key role in Chicago’s last three Stanley Cup wins. We are thrilled to have him join our team."
The 24-year-old Murphy had two goals and a career-high 15 assists in 77 games with Arizona last season. Dauphin, 22, has appeared in 32 NHL games over the last two seasons.
Hjalmarsson gives Arizona more stability on the back end after it traded away No. 1 goalie Mike Smith last weekend. It also decided against re-signing captain Shane Doan after 21 years with the franchise, and then announced Thursday that Dave Tippett was out after eight seasons in a mutual agreement between the coach and the franchise.
Tippett coached the Coyotes through four years of being run by the NHL after the team went into bankruptcy, making the best with a team hampered by financial limitations. The Coyotes reached the 2012 Western Conference final, but have fallen on hard times since, missing the playoffs five straight seasons.
Tippett was given a five-year contract extension and was named executive vice-president of hockey operations in 2015, but had philosophical differences with owner Andrew Barroway.
Hjalmarsson, a fourth-round pick in the 2005 draft, had 23 goals and 120 assists in 623 career games with Chicago. He also holds the franchise record for most playoff games played by a defenceman at 128.