Compel is today expected to announce the three-year contract, which the BBC has the option to extend to seven years.
Although the terms of the deal are confidential, industry experts said it was likely to be worth pounds 18m-pounds 25m a year.
Compel won the contract, which was advertised under European Union procurement rules, in the face of stiff competition from rivals, including Computacenter, the giant distributor.
The contract marks an increasing trend by large companies to outsource all their computer requirements to a single supplier in order to reduce costs and streamline their own information technology departments.
There is a demand for groups which can supply a vast range of computer equipment at competitive prices, while also providing the necessary services to install, integrate and maintain the equipment.
Although Computacenter - which is capitalised at over pounds 1bn - is by far the largest operator in the market, Compel is carving a niche for itself. Its share price has more than doubled in the past 12 months. It closed at 444p on Friday, valuing the group at pounds 125m.
Under the terms of the deal, Compel will supply and service 18,000 PC users in the UK and abroad.