Two-year-old Ahmad and Muhammad Ibrahim have made what doctors described as a remarkable recovery.
Dr James Thomas, director of critical care at Children's Medical Center in Dallas, where the boys were separated on 12 October, told a news conference they would be moved to nearby Medical City Dallas where doctors will work to repair the parts of their skulls under which there lies no bone.
"Considering the tremendous odds they faced preoperatively, these boys have done remarkably well. So many things that could have gone awry, didn't," Thomas said.
A month ago, the boys underwent 34 hours of separation surgery - for which doctors had prepared for a year. In the operation, a team of five neurosurgeons separated brain material they shared as well as the shared circulatory systems that feed blood to their brains.
The boys can now sit upright as they blow kisses, bang on tambourines and give high-fives to doctors and nurses. They have stayed in separate rooms but come together for play time.
In an emotional press conference, the boys' father Ibrahim Muhammad said through an interpreter that the successful surgery was "a miracle."
"I would love to take them back to Egypt with them walking on their own feet"
the twins' father
"I would love to take them back to Egypt with them walking on their own feet," he said.
The boys avoided for the most part post-operative complications such as infection, blood clots, or brain swelling - all of which could have proven fatal.
They have been fitted for special head bands to protect their skulls, and in the coming days, doctors at Medical City Dallas should give some indication as to how they will repair their damaged skulls.
"We expect that they are going to get stronger each day. Many of the neurological problems we anticipated have not occurred, and we are hoping that they continue on their road to recovery," said Dr Ken Shapiro, one of the boys' neurosurgeons.
The cost of the medical procedure was expected to reach about $2 million and be paid for by charity, with many in the medical team donating their services for free.
"They were saying 'bye-bye' to us, and that means a lot to us," Shapiro said as the boys were about to leave the hospital.
The boys were born in a town 800 km (500 miles) south of Cairo on June 2, 2001.