The will sign a partnership agreement with the head of the project, Massachusetts Institute of Technology's Nicholas Negroponte, in the Alpine ski resort of Davos on Saturday, officials said.
Davos is hosting the annual meeting of the World Economic Forum, a gathering of top politicians, economists and business executives.
The aim is to provide the free of charge to children in poor countries who cannot afford computers of their own.
Under the agreement, UNDP and the nonprofit One Laptop per Child organization set up by chairman Negroponte, will work together with local and international partners to in least developed countries.
The goal is for governments or charitable donors to pay for the laptops, although children will own them.
About the size of a textbook, can set up their own wireless networks and operate in areas without a reliable electricity supply, since they can be powered by hand cranking.
Proponents say the devices, which have been welcomed by United Nations Secretary General Kofi Annan, will be a boon for education.
But not everyone is convinced.
Intel Chairman Craig Barrett said last month the world's poor would not want the $100 "gadget," since it will have a limited range of programs and capabilities.