The New York State Athletic Commission voted Wednesday to approve rules and regulations governing combat sports, finalizing a bill that will make New York the 50th U.S. state to legalize professional mixed martial arts.

The law marks a huge victory for mixed martial arts and its purveyors, most prominently the Ultimate Fighting Championship. But not everyone it governs is pleased. Some elements in the law, ostensibly included to make combat sports safer, will threaten the business of professional boxing in New York, according...