NHS Scotland has signed the £110m six-year deal with Capita to set up a single shared information network across the public sector.
However, the NHS still faces legal action from BT, which is believed to be pursuing £20m in damages. The firm claims the tendering process was flawed.
More than 4600 sites will be connected to the Scottish Wide Area Network (Swan) including schools, hospitals, GP surgeries, pharmacists and council offices under the first phase of the work.
Those behind the move say the new network will make it easier and more secure for information to be shared by public organisations, and that it will cut costs arising from the numerous contracts with different firms.
NHS National Services Scotland (NSS), which led the negotiations, said the initial value of the contract is £110m, rising to a potential £325m as more organisations joined the shared system.
Ian Crichton, chief executive of NHS NSS, said: "Following extensive dialogue over the last year, I am pleased to announce the award of the Swan contract to Capita. This was the strongest bid and offers excellent value for money for the public purse.
"Swan is a major step forward in Scottish public sector infrastructure which will create major savings and deliver an excellent service. Swan is a good deal for the Scottish taxpayer and anyone who uses public services, whether in schools, councils, hospitals or elsewhere."
The awarding of the contract was delayed when a dispute broke out at the end of last year as the NHS was preparing to award the contract and end the one it had with BT.
The telecoms giant, which was also bidding for the new contract, launched a lawsuit against the NHS claiming the tendering process was flawed. After a hearing at the Court of Session Lord Malcolm ruled the NHS could proceed with the deal from Capita.
While BT decided not to appeal the ruling, the company last week said it would still pursue damages, believed to be £20m.
BT said that its tender offered "excellent value and minimal risk to Scottish taxpayers" and believed that it was unclear "whether the most economically advantageous tender" would be awarded.
In a statement, BT said: "We are pleased that Lord Malcolm, following the hearing in January, found in our favour with respect to the primary argument and agreed that the procurement regulations had been breached by NHS NSS.
"Though BT's primary aim was always to seek a re-run of the procurement process, the case will now proceed as a damages claim, Lord Malcolm having found damages to be an appropriate remedy for BT to seek for that breach."
The awarding of the contract comes as the Scottish Government is integrating the NHS and council-run social care services.
The Scottish NHS, Education Scotland, and seven councils - Highland, Argyll & Bute, Moray, Orkney and Western Isles, Dumfries & Galloway and Scottish Borders - are involved in the first phase of Swan, but it is hoped this will expand significantly.
The contract is due to start in April, although NSS suggests the legal delay has created a backlog.
Three companies were involved in the final selection stage of the bidding process - Cable & Wireless together with Virgin Media Business, Capita plc, and BT.