Their statements come just three days ahead of the oral hearing before the ICJ, the principal judicial organ of the United Nations (UN).
Both countries "will abide by and implement the ICJ ruling which settles our ongoing dispute at this international court of justice," Humala said in a joint statement to the media.
For his part, President Piñera said "Chile has been, is and will remain a country that respects international law, the peaceful resolution of disputes, treaties and international courts."
The heads of state highlighted the importance of working on a common agenda after the ICJ ruling, with the aim of "strengthening bilateral integration for the benefit of the two peoples."
President Piñera said he discussed with his Peruvian counterpart about ways to further strengthen the ties of unity, friendship and cooperation between Peru and Chile, "and we have a broad and very successful agenda."
"For these reasons, I reaffirm the willingness of the government and people of Chile to strengthen and increase the ties that bind us to the Peruvian people," he said.
Humala and Piñera met on the sidelines of the 6th Regular Meeting of the Council of Heads of State and Government of the Union of South American Countries (Unasur), which is being held in Lima.