Veloso, a 39-year-old former domestic helper and mother of two, told reporters in Jakarta she was ready to start a new life in the Philippines.
Veloso was arrested in Yogyakarta in 2010 after being found with 2.6 kg (5.73 lb) of heroin concealed in a suitcase. She said she was an unwitting drug mule, but she was convicted and sentenced to death.
Her release came days after the five remaining members of the "Bali Nine" drug ring were repatriated to Australia from Indonesia.
Veloso was flanked by heavy security upon her arrival at Manila's airport and was transported straight to a prison facility for women. Her family and dozens of supporters who were waiting outside the terminal failed to greet Veloso on her arrival.
Prison guards later allowed Veloso's family to spend time with her. Veloso's two sons ran towards her and hugged her tightly as they met inside the prison compound.
"I'm so happy I'm able to come home to our country. I appeal to the president that I be given clemency," Veloso told reporters.
The two governments agreed this month to transfer Veloso back to Manila in a deal that includes the Philippines respecting the court's sentencing of Veloso and her status as prisoner.
Any decision on her clemency will depend on Philippine President Ferdinand Marcos Jr. But a justice ministry official said on Wednesday the Philippine leader would consider her case.
"Definitely, that's on the table," Justice Undersecretary Raul Vasquez told reporters.
Indonesia had previously said it would respect any decision made by the Philippines, including if Veloso was given clemency.
Philippine Foreign Minister Enrique Manalo thanked the Indonesian government for its "sincere and decisive action" to allow Veloso to return home in time for the Christmas holidays.
"Their generosity has made possible this momentous day of Ms. Veloso's return to the Philippines," Manalo said in a statement.
