More than 34,000 homes and businesses in the two cities stand to benefit from the investment by BT.
The new system means that, in theory, families will have the technology to watch high definition television through computers, or work from home using high quality video conferencing.
BT is spending 1.5 billion by 2012 to ensure 40 per cent of UK homes and businesses have access to superfast broadband. The new technology uses fibre-optic cables instead of traditional copper wires, which can provide broadband speeds of up to 40 megabits per second (MBPS).
At present, most users are signed to deals promising 8MBPS, but the average speed is less than half that.
In Edinburgh, the new service will be available initially to some 4,000 customers in the Stockbridge and New Town areas.
More than 30,000 homes and businesses around Glasgow University and in the city's Hillington Park business and industrial area will also be among the first to benefit.
However, Ofcom has refused to impose regulatory barriers on the roll-out of the new technology, meaning it is likely the costs of implementing the new networks will be passed on to customers.
Steve Robertson, the chief executive of Openreach, the BT division responsible for the delivery of the plans, told delegates at a Scottish Council for Development and Industry (SCDI) conference in St Andrews yesterday that the first phase of the new technology should be available early next year.
He said: "Superfast broadband is essential to Scotland's future, so it is great to announce this initial set of locations.
"Once again, Scotland is at the forefront of one of the most important projects to take place in recent years. It will play a vital role in the UK's future as a knowledge-based economy."
Work in Edinburgh and Glasgow will begin in early summer, and the new networks will be up and running by early 2010. BT said it would work with utility companies to minimise any disruption during the work.
Alex Salmond, the First Minister, said broadband was already available in 99 per cent of Scotland, and added: "This technology has quickly established itself as vital communications tool for businesses and people of all ages.
"This new service will give customers in two of the country's biggest cities even greater access to the opportunities and services that the internet offers."
Dr Lesley Sawyers, the chief executive of the SCDI, said: "We will be working with the company to identify how more of the country can benefit in the near future."
Jenny Dawe, the Edinburgh city council leader, and Steven Purcell, her Glasgow counterpart, both welcomed the decision.
But Liam McArthur, the Liberal Democrat MSP for Orkney, pointed out that remote and island communities had no access to broadband, or had a service offering slow speeds.
"Unless the government acts to get the improvements rolled out quickly across Scotland, a dangerous chasm risks opening up between the digital haves and have-nots," he warned.