The first batch of computers built for the One Laptop Per Child project could reach users by July this year.
The laptop could one day cost as little as $100
The scheme is hoping to put low-cost computers into the hands of people in developing countries.
Ultimately the project's backers hope the machines could sell for as little as $100 (£55).
The first countries to sign up to buying the machine include Brazil, Argentina, Uruguay, Nigeria, Libya, Pakistan and Thailand.
The so-called XO machine is being pioneered by Nicholas Negroponte, who launched the project at the Massachusetts Institute of Technology's Media Lab in 2004.
Test machines are expected to reach children in February as the project builds towards a more formal launch.
Mr Negroponte told the Associated Press news agency that three more African countries might sign on in the next two weeks.
The laptop is powered by a 366-megahertz processor from Advanced Micro Devices and has built-in wireless networking.
It has no hard disk drive and instead uses 512 MB of flash memory, and has two USB ports to which more storage could be attached.
"I have to laugh when people refer to XO as a weak or crippled machine and how kids should get a "real' one"," Mr Negroponte told AP.
"Trust me, I will give up my real one very soon and use only XO. It will be far better, in many new and important ways."
The computer runs on a cut-down version of the open source Linux operating system and has been designed to work differently to a Microsoft Windows or Apple machine from a usability perspective.
Instead of information being stored along the organising principle of folders and a desktop, users of the XO machine are encouraged to work on an electronic journal, a log of everything the user has done on the laptop.
The machine comes with a web browser, word processor and RSS reader, for accessing the web feeds that so many sites now offer.
"In fact, one of the saddest but most common conditions in elementary school computer labs (when they exist in the developing world), is the children are being trained to use Word, Excel and PowerPoint," Mr Negroponte said.
"I consider that criminal, because children should be making things, communicating, exploring, sharing, not running office automation tools."
The new user interface, known as Sugar, has been praised by some of the observers of the One Laptop Per Child project.
It doesn't feel like Linux. It doesn't feel like Windows. It doesn't feel like Apple," said Wayan Vota, who launched the OLPCNews.com blog and is also director of Geekcorps, an organisation that facilitates technology volunteers in developing countries.
"I'm just impressed they built a new (user interface) that is different and hopefully better than anything we have today," he said.
But he added: "Granted, I'm not a child. I don't know if it's going to be intuitive to children."
Trial versions of the operating system in development can be downloaded to be tested out by technically-minded computer users around the world.