The 55-year-old billionaire entrepreneur is expected to close on the purchase from Andrew Barroway, the Coyotes' sole owner, next month.
Barroway will retain a 5 percent minority share once the sale is final.
"He's committed to trying to get a new arena in the right location and making it work," NHL Commissioner Gary Bettman said of Meruelo. "He is a person of substantial means and he's very good if you look at his career in turning around businesses and making them successful. I think this is an extraordinarily positive step for the Coyotes and their fans in Arizona."
Coyotes president and CEO Ahron Cohen said the approval was unanimous in a statement released by the team.
"The Board of Governors' unanimous approval today represents a major milestone for the Coyotes organization, our great fans and, of course, for Mr. Alex Meruelo," Cohen said. "Our expectation at this time is that this transaction will close later in July. As we move forward, our team will do everything we can to continue building the positive momentum and progress we have achieved on and off the ice. We are determined to make this summer a success as we head into the 2019-20 season. We will keep Our Pack updated on further milestones in this process."
The NHL is hoping Meruelo will be able to secure a deal for a new arena to be built for the Coyotes, ideally in the East Valley of the Phoenix metropolitan area. A new arena for Arizona is a priority for the NHL.
Commissioner Bettman twice said the Coyotes would not be able to remain at Gila River Arena in Glendale on a long-term basis. He didn't want to discuss the possibility of the Coyotes having to relocate to another market because of the optimism Meruelo has in his ability to get an arena built.
"He has told us, including in his interview with the [BOG] executive committee, that he very much likes Arizona, he wants to make it work there and he's going to try very hard for that to be the case," Commissioner Bettman said. "Obviously, the club is not viable long term in Glendale, but hopefully we don't get to that point."
Meruelo, the son of Cuban immigrants, was born in New York City and grew up in Los Angeles. He is the sole owner of Meruelo Group, a construction and real estate development firm, and is the owner of SLS Las Vegas, formerly the Sahara Hotel and Casino, and Grand Sierra Resort in Reno, Nevada.
Barroway became the Coyotes majority owner in 2015 and bought out his partners in 2017 to become the sole owner.