Mr Beatie began taking testosterone in 1979 and underwent a double mastectomy in 2002.
Mrs Beatie said the couple's roles would not change once the baby was born.
Viewers across the US on Thursday saw footage of Mr Beatie's ultrasound scan and heard a heartbeat.
The baby would be "daddy's little princess", said Mr Beatie, who described himself as a tomboy growing up.
Nancy Beatie's lawyer David Higgins said Judge Gerlach's decision was thorough but not the one she had hoped for.
In his ruling, Judge Gerlach wrote that the couple had failed to prove Mr Beatie was a male when they were married.
"I'm clearly a man: socially, legally, psychologically, physically - the whole ball of wax, " Mr Beatie told the Arizona Republic in December.
In 2008, Mr Beatie, who had lived as a man for decades, gave birth to a girl, the first of three pregnancies.
Mr Beatie halted testosterone treatments so he could give birth to his children after the couple found out his wife could not get pregnant.
They spoke of their admiration for their mother and Mr Beatie.
"I opted not to do anything with my reproductive organs because I wanted to have a child one day, " a thinly bearded Mr Beatie told Oprah Winfrey.
They revealed Mr Beatie - a former Hawaiian beauty queen - had conceived by artificial insemination, carried out with a syringe by his wife in their home, with sperm purchased from a bank.
Mr Gordon said Mr Beatie, 39, was legally married as a man and never was required to disclose that he retained female reproductive organs when applying for the birth certificate in Hawaii as a man.
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