The decision by the Minnesota State High School League will take effect in the 2015-16 school year, making the state the 33rd to adopt a formal transgender student policy.

The board set out criteria for determining whether transgender students who were born male but identify as female can be eligible for girls’ teams at the nearly 500 schools in the league’s membership. State law already permits girls to compete in boys’ sports.

Religious-affiliated private schools will be exempt from complying with the league’s new language.

The new process for establishing eligibility will include written statements from a student’s parents or guardians and health care professionals regarding the student’s “consistent or sincerely held gender-related identity.”

A school’s activities director will make the eligibility decision, with appeals heard by an independent hearing officer.

The vote capped what league Executive Director Dave Stead called a “long and tangled process” involving several draft versions of the policy and dozens of speakers appearing before the board. Hundreds of responses were submitted to the league’s website.

When the measure passed, supporters — who along with opponents packed the board’s Brooklyn Center offices — erupted in cheers.

Eighteen of the 20 board members voted yes. Emmett Keenan, activities director at St. Cloud Cathedral, voted no. Paul McDonald of Ely, who was appointed by Gov. Mark Dayton and participating in his first board meeting, abstained.

“The religious example is there in statute and in principle, but I do think it needs to be spelled out a little bit more,” Keenan said. “And I’m not sure we’ve heard enough yet about the safety of girls in relationship to a transgender male-to-female playing on girls’ sports teams.”

Other board members were driven by a belief that schools want guidance and consistency from the league.

Chris McDonald, a league board member and debate coach at Eagan High School, said gay, lesbian, bisexual and transgender students “look to this board to provide equal access for all students.’’

Monica Meyer, executive director at OutFront Minnesota, which advocates for transgender issues, said, “All students want is a safe place to just be who they are. That includes in the classroom, on the court or field.”

It’s unclear how many transgender athletes will benefit. Without providing numbers, OutFront Minnesota Communications Director Jean Heyer said, “We have heard trans kids are playing sports right now, and we have heard that there are kids who will try out now that the policy is in place.”

Estimates by the Transgender Law Center in California put 0.3 percent of the population as transgender.

The overflow crowd Thursday surpassed the turnout of about 150 people who attended a transgender policy discussion at October’s board meeting. Supporters and critics filled the room a half-hour before the 9:30 a.m. meeting started, greeting board members by holding signs aloft.

“ALL kids deserve respect,” read 8½-by-11 printed signs provided by Transforming Families.

One woman held up a sign saying, “We represent God.” Someone next to her held up a smaller one reading, “No you don’t!”

About 20 speakers addressed the board. The speakers included transgender students, delegates of advocacy groups and state legislators.

The board’s decision left some opponents seething. At least one person told board members after the vote that they would be judged.

The Minnesota Family Council, a Christian-based advocacy group that says it promotes and defends biblical principles in public policy matters, proposed a bylaw change stipulating that a student’s sex at birth be used to determine eligibility. It wasn’t considered.

Autumn Leva, director of legislative affairs and communications for the Family Council, said the proposal was backed by a petition of “more than 5,500 people” and a mix of 28 public and private high schools. She said those groups were being “excluded from the discussion.”

The board’s vote also added transgender language to its fair hearing procedure, a process typically used to resolve eligibility questions.

Stead acknowledged that support for the policy wasn’t unanimous among the league’s member schools.

“I’ve heard from a limited number of schools that say, ‘I don’t like the idea,’ and then once we’ve talked about it they said, ‘I still don’t like the idea, but I’m supportive of the initiative of trying to give us direction,’ ” Stead said. “There was nothing that was done today that would prevent a school from being a member of the High School League. Not one scintilla.”