Deputy First Minister Nicola Sturgeon made the announcement in Glasgow today.
She said the jobs would be created in areas such as e-commerce, engineering, social media, tourism, laser technologies, cyber security and research and development.
The investment would also help job seekers, older people and those with disabilities gain access to employment.
The jobs are expected to emerge over the next 15 years as the Scottish Government invests in providing faster, next generation broadband access for businesses and communities.
The money from the Government includes £120m specifically for the Highlands and Islands and £5m to assist community groups in rural areas gain access to broadband networks.
Ms Sturgeon, who is also Infrastructure, Investment and Cities Secretary, revealed the news after visiting Stream Communications near Charing Cross, a European leader in the design and provision of highly specialised mobile network services.
Ms Sturgeon said: "Scotland has huge strengths in areas such as renewables and life sciences. I want our digital industry to be a similar driving force for our economy.
"The huge potential and massive opportunities are clear. In addition to creating about 800 jobs building the infrastructure over the next five years, the investment in improving Scotland's digital connectivity is forecast to support around 14,000 jobs in the wider Scottish economy over the next 15 years."
She said the investment in the digital economy would transform Scottish businesses, raising productivity and opening up new markets to attract inward investment.
Ms Sturgeon added: "It will also change the way we live – from the way we book holidays to the way we access health care. We are committed to ensuring all of Scotland is able to reap the social and cultural benefits of the internet.
"Broadband, just like roads and railways, is a vital part of Scotland's infrastructure, and that is why we are committed to delivering a world class digital infrastructure to the people of Scotland by 2020."
Nigel Chadwick, director of Stream Communications, said: "Our new lab, the first of its kind in Europe, is at the forefront of technical innovation in the design and provision of specialist mobile network services."
Lena Wilson, chief executive of Scottish Enterprise, said the investment in Scotland's digital infrastructure was key to maintaining companies' global competitiveness.
She added: " It also allows us to build on our existing world-class reputation for creating innovative businesses and offers an additional compelling incentive for inward investors."