Castan had a three-and-a-half-hour operation to remove a cavernoma from his brain on Tuesday, with Roma confirming afterwards that the procedure had been successful.
And the Serie A club released a further statement on Wednesday to reveal the 28-year-old Brazilian is out of intensive care and "progressing as expected".
"Leandro Castan has successfully negotiated the first 24 hours after his operation," it read.
"He is conscious and interacting with family members and medical staff. He has now left the intensive care unit, but is still being constantly monitored.
"He is progressing as expected, though no prognosis has yet been released."
Castan was diagnosed with the problem after reporting he was feeling dizzy following Roma's 1-0 victory over Empoli in September.
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