Terms of the deal weren't disclosed, but a source told ESPN's Pierre LeBrun that the average annual salary of the deal is $5.475 million.
"I am very happy to join the Coyotes," Goligoski said in a statement. "Arizona is a great place to live and play and I'm excited to join an up and coming team that has a ton of talent and a very bright future."
The Coyotes acquired the negotiating rights to Goligoski in a trade last week with the Dallas Stars for a fifth-round pick in this week's draft.
Goligoski, 30, was potentially one of the top free-agent defensemen available on the market and had 37 points in 82 games last season with the Stars.
Dallas tried to re-sign Goligoski but failed to agree to terms. His signing is the first made by Arizona's new general manager, the 27-year-old John Chayka.
"We are thrilled to sign Alex to a long term contract," Chayka said in the statement. "Alex is a great skater and a smart, efficient defenseman who moves the puck well and makes his teammates better. He will help solidify our defense and support the growth of our young players."