As part of the deal, CGI will create a Scottish Centre of Excellence in the region.
Scottish Borders Council described it as the "most significant" inward investment proposal the region had ever known.
It said the deal had been enabled by the Borders Railway which officially opened last year.
The agreement sees SBC award its digital services contract to CGI.
The 13-year contract will provide the authority with "state-of-the-art technology to deliver excellent customer services and streamlined systems".
The council said it had the potential to inject more than £100m into the local economy.
Apart from a centre of excellence being created in the Borders, the deal will also mean that the council's existing 49 information and communications technology (ICT) staff will remain in the region.
"CGI is committed to working with a diverse range of partners to help bring flexible, cost-effective digital solutions to local and central government across the UK."
Are you looking for a new software career opportunity? Scotland has a lot to offer, with a growing technology sector and a range of major international companies and ambitious homegrown companies that you can work for.
Find out how you can grow your software career in Scotland