The 2020 tournament is being co-hosted by Colombia and Argentina, the first to be held jointly by two nations.
Duque made the surprise announcement in Bogota and thanked Argentina President Mauricio Macri for his support.
"I think Colombia will now have another reason to be happy," Duque said.
The 2020 Copa America will be the fourth in six years.
The tournament brings together the 10 South American nations and two invited guests, which next year will be Qatar and Australia.
One of the two visiting nations will be drawn in the Colombia-based northern section along with Colombia, Brazil, Venezuela, Ecuador and Peru.
The other will be drawn in the Argentina-based southern section along with Argentina, Paraguay, Uruguay, Bolivia and Chile.
Four will qualify from each section for the quarter-finals.
The venues for the opening match and the semi-finals have not yet been revealed.
The 2019 Copa America continues with the opening quarter-final between hosts Brazil and Paraguay later on Thursday.
(Reporting by Andrew Downie in Sao Paulo; Editing by Ian Ransom)
