The five-year deal promises to bring additional bandwidth and improved network speeds in buildings such as schools, libraries, offices and remote sites across a 340-square mile area.
It is said the improved access would result in better services for local communities, helping job seekers and people seeking online training, as well as enhanced connections in rural areas.
It has been claimed it could cut the council's annual telecommunications bill by more than 20%. Savings of £120,000 per year are expected, with the authority benefiting from data sharing opportunities with other government agencies.
The improved service means the council will also be able to introduce flexible working for staff.
Capita IT Services will be working with North Ayrshire Council's wide area network (WAN) specialist partner, Updata Infrastructure, on the contract.
Peter Hands, managing director at Capita IT Services, said: "The new network will be the foundation of delivering the council's transformation programme, which aims to provide enhanced services to the local community quickly and cost effectively.
"We look forward to supporting the delivery of numerous benefits to the social and economic livelihoods of North Ayrshire's communities."
Richard Parkinson of FarrPoint, which developed the business case for the council and acted as technical advisors on the procurement process, said: "Network technology such as this can really make a difference in terms of connecting people and services, and ultimately allowing for efficiency savings. We have been pleased to work on a project that will see the technology making a real difference."