In court, Houston testified that she did not need spousal or child support and that the couple's 14-year-old daughter, Bobbi Kristina, could not depend on Brown.
"He's unreliable," Houston told the judge. "If he says he's going to come, sometimes he does. Usually he doesn't."
Houston declined to comment to reporters after the hearing.
Brown's attorney, Ram Cogan, said he will seek to overturn the judge's decision.
Houston filed for divorce in October, citing irreconcilable differences. She was granted a default judgment in December to speed up the divorce. Miller's ruling Wednesday upheld the terms of that judgment.
Houston and Brown wed in 1992, when she was at the height of her fame as a Grammy-winning superstar known for such hits as "I Will Always Love You."
During their tumultuous marriage, Brown was arrested on drug and alcohol charges, and Houston twice entered drug rehabilitation programs.