In October, IceArizona agreed to sell the majority stake to Barroway for US$155 million.
"This is truly a dream come true for me and my family," Barroway said in a team statement. "I am extraordinarily grateful for the opportunity of a lifetime and look forward to working and solidifying a strong partnership with the club's current ownership group.
"As a group we are committed to serving our fans with a new level of excellence and our collective goal is to put a competitive team on the ice every season and, one day, win the Stanley Cup."
IceArizona bought the money-losing franchise last year from the NHL, which had been running it since Jerry Moyes took the team into bankruptcy in 2009.
Barroway is the managing partner of Merion Investment Management LP, an event-driven hedge fund that manages more than $1 billion. He previously tried to buy the New Jersey Devils and New York Islanders.
Barroway replaced George Gosbee as the team's chairman and governor.
"Today is an exciting day for the Arizona Coyotes and our great fans," said Anthony LeBlanc, the team's part owner, president and CEO. "The addition of Andrew Barroway to our ownership group further solidifies the Coyotes long-term future in the Valley. Our entire ownership group is excited about this opportunity to work with Andrew in taking this franchise to the next level."