Rambold admitted having sexual relations with Cherice Moralez, then 14, in 2008 while he was her high school teacher. Moralez committed suicide before her 17th birthday.
The Billings Gazette reported Rambold left Montana State Prison about 9 a.m. MDT.
The Montana and Pennsylvania chapters of the National Organization for Women and a women's rights group called Ultraviolet filed a complaint Tuesday with a judicial review board, asking that Baugh be removed from the bench, KULR-TV, Billings, reported.
More than 140,000 people signed accompanying petitions, the groups said.
Prosecutors called the sentence illegal and appealed it to the high court.
The case drew wide attention when Baugh imposed a one-month sentence on Rambold and made controversial comments about the victim, saying she "seemed older than her chronological age" and she was "as much in control of the situation."
Baugh later apologized and tried to resentence Rambold, but the state Supreme Court said he lacked standing to change a sentence.
Besides the 31-day prison term, Rambold was sentenced to probation for 14 years and 11 months.
With Cherice's death, the prosecution entered into what is known as a "deferred prosecution agreement" with Rambold, CNN reported.
The agreement meant all charges against Rambold -- who admitted to one of the rape charges -- would be dismissed if he completed a sex-offender treatment program and met other requirements, one of which was not having contact with children.
Prosecutors said the former teacher didn't uphold the agreement and asked Baugh last month to sentence him to 20 years.
Baugh ruled Rambold's infractions weren't serious enough.
"He made some violations of his treatment program," the judge said. "They were more technical and not the kind you would send someone to prison for."