It paves the way for a circuit to connect data centres serving the new site, the existing hospital and Dumfries and Galloway Council.
The project comes to a close seven months ahead of the opening of the new hospital.
It aims to allow the health board and council to deliver "efficient, technology-enabled services."
Julie White, chief officer for the health and social care partnership, said the project had ensured best value for the public purse.
"We are now one step closer to opening a new hospital designed and constructed to utilise the most advanced information technology," she said.
"We would like to thank everyone involved for their efforts to deliver this project on time, on budget, and with minimal disruption to the public"
Robert Moore, construction services director with Boston Networks, said it was delighted to be working on the new fibre optic network.
"The network will provide high bandwidth connectivity between the council and NHS, and will support the delivery of advanced technologies within the new facilities to further augment the efficient and effective treatment of patients," he said.
Months of work to install a seven-mile long cable as part of a new hospital scheme in Dumfries have been completed.