Nathaniel Santos Batista Junior, a jurist who helped draft the document, said the idea was to protect their rights in case of separation or death of a partner, Globo reports.
Ms Domingues, who is based in the Sao Paulo city of Tupa, said the move reflected the fact that the idea of a "family" had changed.
"We are only recognizing what has always existed. We are not inventing anything."
"For better or worse, it doesn't matter, but what we considered a family before isn't necessarily what we would consider a family today."
But lawyer Regina Beatriz Tavares da Silva told the BBC it was "absurd and totally illegal", and "something completely unacceptable which goes against Brazilian values and morals".
Ms da Silva, who is president of the Commission for the Rights of the Family within the Institute of Lawyers, says the union will not be allowed to remain in place.
Some religious groups have also voiced criticism of the move.
While Ms Domingues has approved the union, it is not clear whether courts, service providers and private companies such as health insurance providers will accept the ruling.
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