The $25 (£16) machine is being created in the hope that it will inspire a new generation of technology whizz kids.
The Pi uses an Arm chip similar to that found in mobile phones and is intended to run a version of the Linux open source operating system.
Test versions of finished devices are being checked and if all is well volume production will start in January.
The idea for Raspberry Pi came from video game veteran David Braben who was searching for a way to inspire young people to start a career in technology.
Mr Braben got his start in games thanks to the BBC Micro on which he, and school friend Ian Bell, created pioneering computer game Elite.
Raspberry Pi is being developed in Cambridgeshire and every update has been watched closely by those keen to get working with the gadget. Raspberry Pi took to its blog on 23 December to report that the first finished circuit boards had arrived.
The batch of bare bones circuit boards are the first to be populated with all the components making up the finished device. The batch is undergoing electrical, software and hardware testing to ensure all is well in the production process.
“Once we’re happy that this test run is fine, we’ll be pushing the button immediately on full-scale manufacture in more than one factory,” wrote Liz Upton on the blog.
The finished device will be sold in two configurations. A Model A for $25 (£16) which lacks a network connector and a Model B for $35 (£22) which does have an Ethernet socket.
Ms Upton said if the tests go well the first batch of 10 boards will be auctioned off to the highest bidder.
Raspberry Pi initially intended to finish its machine by the end of 2011. However, it said, delays in development meant it was now about three weeks behind schedule.
Despite this, it anticipates that people will be able to place orders for the gadgets in early January. No pre-orders have been taken because the organisation said it did not want to take anyone’s cash without having something to hand over in return.