Last Friday Veloso was sent to Nusakambangan prison island, where the executions were to be carried out, sparking last-ditch appeals by the Philippines.
On Monday, Mr Aquino met Indonesian officials, including President Joko Widodo, on the sidelines of a regional meeting in Malaysia to discuss Veloso's case.
Philippine officials said that the next day, hours before Veloso was due to be executed, Mr Aquino called Indonesia's Foreign Minister Retno Marsudi. Mr Aquino proposed keeping Veloso alive so that she could testify against drug traffickers.
Mr Aquino spoke to Mr Widodo on the sidelines of the Asean leaders summit in Kuala Lumpur on Monday
Around 11:00 local time (06:00 BST) on Tuesday, Ms Sergio is reported to have shown up at a police station in the Philippines.
Her appearance seems to have sealed the deal. Indonesia gave Veloso an 11th-hour reprieve, saying she was needed to testify against a "perpetrator suspected of human trafficking".
Since 2010, Veloso and her family have said Ms Sergio was to blame for Veloso's situation.
Philippine police also recently said their investigations found that Veloso may have been tricked, and recommended that charges be brought against Ms Sergio and two others.
But Ms Sergio has also maintained her innocence, saying she was only helping Veloso look for a job.
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