<... Public Notary Claudia do Nascimento Domingues has said the man and two women should be entitled to family rights.
She says there is nothing in law to prevent such an arrangement.
But the move has angered some religious groups, while one lawyer described it as "absurd and totally illegal".
The three individuals, who have declined to speak to the press, have lived in Rio de Janeiro together for three years and share bills and other expenses.
Ms Domingues says they have already opened a joint bank account, which is also not prohibited by any law.
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We are only recognising what has always existed, we are not inventing anything_
Claudia do Nascimento Domingues
According to Globo TV, the union was formalised three months ago, but only became public this week.
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 recognising 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.