Lula, 79, remains under observation in intensive care in the Hospital Sirio-Libanes in Sao Paulo following the emergency operation carried out on Tuesday. His doctors have said he should be released next week.
Lula "has progressed well in the immediate post-operation phase, without incident," the hospital said in a public medical update.
"He is alert, engaged, conversing and spent the night well," it said.
The president was taken from Brasilia to the Sao Paulo hospital late Monday after complaining of a headache, which an MRI scan determined to be an intracranial hemorrhage.
The emergency was linked to a blow to the head Lula suffered on October 19 when he fell in a bathroom in his presidential residence. That fall necessitated stitches and Lula at the time said it was "serious".
The leader, who returned to power in January last year, skipped planned overseas trips following the fall, but from mid-November resumed his active schedule, hosting a G20 summit in Rio and attending a Mercosur summit last week in Uruguay.
His medical team told a news conference on Tuesday that the cranial bleeding was between his brain and the dura mater protective membrane under the skull.
Surgeons performed a trepanation -- drilling into his skull to relieve the pressure.
The doctors said he suffered no brain damage from the hemorrhage and should be permitted to leave the hospital to return to Brasilia next week.
