The ruling won't take effect for at least 10 days, but both the adoption agency and the biological family could fight the decision, potentially delaying the boy's move.
Megan Lynn Morgan of Sutherland, the boy's birth mother, had said she wanted her son to be an only child with the adoptive family and that she wanted an open adoption, an arrangement that grants biological parents many rights.
The Veselys, of Verdigre in northeast Nebraska, said they planned to tell Morgan that Angela was pregnant but were waiting because she had previously miscarried three children. She later gave birth prematurely, but the child is now at their home.
Kelly Tollefsen, one of the Vesely's lawyers, said the couple welcomed Friday's ruling.
"The Veselys are obviously excited and want to get Morgan back in their home as soon as possible," Tollefsen said. "They were very happy and elated."
P. Stephen Potter, who represents the Morgans, said he still needed to meet with his clients to discuss the ruling.
"I'm sure they'll do everything they can to maintain custody of the child," he said.
A spokeswoman for the Children's Home said Friday that officials planned to fully evaluate the ruling before deciding how to respond.
The Veselys applied to adopt in 2005, and Jason Vesely has said his wife was more than four months pregnant when the agency assigned the child to them in late 2007.
The boy lived with the Veselys from the time he was 4 days old until a Knox County district judge ordered him removed in February at 3 months. The agency placed him with the biological mother's parents in Sutherland in central Nebraska.
The boy has been known by two different names. The Veselys called him Morgan Jason Vesely, but the Morgans called him Brett Jonathan Morgan.
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On the Net:
Nebraska Children's Home Society: http://www.nchs.org
Nebraska Judicial Branch: http://www.supremecourt.ne.gov