Judge Barbara Walther's order places the children in 16 foster-care facilities scattered across Texas.
The judge's order states that teenage mothers will be placed with their babies. Teenage pregnant girls will be placed alongside those young mothers.
Children under 12 months will be placed in foster homes with their siblings who are under 5 years. Boys 8 years and older will be in the same setting as older boys.
"Every attempt will be made to place siblings together," the order states.
A spokesman for the Fundamentalist LDS Church was outraged by the judge's decision.
"Every step in this proceeding the court has acted without regard to the rights or wishes of the people whose lives are affected here," said Rod Parker, a Salt Lake City attorney who is speaking on behalf of the FLDS people.
At least two requests for a temporary restraining order were filed in court in San Angelo, trying to stop the removal of the children from the coliseum.
The judge has not even heard the motions in court, said an attorney who filed them.
"My clients are absolutely distraught," said Julie Balovich, with the Texas Rio Grande Legal Aid, who represents a group of FLDS mothers.
Balovich questioned whether the children will truly be placed with siblings, noting that one of her clients has five children and three of those children will be going to different homes.
The first bus filled with children left the coliseum just before 1 p.m. Tuesday, escorted by police cars and ambulances. About half a dozen charter buses some filled with children, some not left the coliseum at various intervals for the next hour. Children seen inside some of the buses waved at reporters and cameras as they drove off.
The coliseum, where 437 children taken from the FLDS Church's YFZ Ranch were being held, was locked down as the children were bused away. Attorneys were kept locked inside. The lockdown was lifted about 2:15 p.m. Central time. Moments afterward, a Tom Green County sheriff's van drove out of the coliseum parking lot with two FLDS women inside who looked visibly upset.
The women were reportedly dropped off at the YFZ Ranch.
Child welfare workers have said they would be placing the children in foster care once they finished taking DNA samples from the children. That process is still under way today.
In nearby Eldorado, FLDS mothers and fathers showed up at the Schleicher County Memorial Building to give DNA samples.
"I don't know why I should have to do this. I have documents," said an FLDS man as he left the building.
A judge ordered the DNA samples to establish parentage after child welfare workers complained that they have been unable to get accurate names or ages of the people in custody.
Copyright 2016, Deseret News Publishing Company