Infrastructure Secretary Nicola Sturgeon said the non-stop journey on trains travelling at up to 140mph would be facilitated by a dedicated track constructed over the next 12 years which would link to a £33 billion network of high-speed routes being planned in England.
However, she was accused by Labour of committing to a multibillion-pound rail scheme without knowing how much it would cost after saying specific route options, including the potential location of new rail terminuses to accommodate the 400m-long trains, are expected to emerge only next year when detailed planning gets under way.
Her announcement, made at the start of a two-day conference on high-speed rail, comes four months after the Scottish Government watered down a £1bn rail investment programme which would have seen the fastest journeys between Glasgow and Edinburgh cut from 50 minutes to 37.
The fastest intercity journey is now expected to be 42 minutes following £350m of cuts to the Edinburgh Glasgow Improvement Programme, which will see the main line via Falkirk electrified by 2016.
The UK Government is committed to building a high- speed line, known as HS2, between London and Birmingham and is due to announce how it will extend the Y-shaped network along separate branch lines to Manchester and Leeds by the end of this year.
Speaking in Glasgow's Central Station, Ms Sturgeon said she would not wait "for Westminster to bring high-speed rail to us". She added: "We now know that within just 12 years, we could build a line which will see journey times between our two major cities cut to less than half-an- hour. That will benefit our businesses, our jobs market and also our tourism industry. And it will put us up there with the world's greatest transport networks."
However, Richard Baker, Labour's Shadow Infrastructure Secretary, said: "This announcement is a great headline grabber, but the devil is in the detail.
"The Scottish Government is now committing itself to a rail upgrade when it doesn't even know how much it will cost. Long-suffering passengers will also remember the SNP has axed the previously announced plans to dramatically reduce the travel time earlier this year."
In March, Justine Greening, the former UK transport secretary, agreed a timetable with the Scottish Government for extending a high-speed rail route to Scotland by 2015. Under current plans, journey times between London and Scotland are expected to be improved by less than an hour as on the northern half of the journey trains will have to slow down considerably.
The new Glasgow-Edinburgh route is expected to link to the proposed new cross-border service. David Simpson, Network Rail's route manager for Scotland, said the Scottish Government's announcement made it more likely a Y-shaped route similar to the existing West Coast main line would emerge as the preferred option. "I think that's the case. The work Network Rail did on high-speed rail in 2008 concluded a Y-shaped network was the best option to get from London to Glasgow and Edinburgh," he said. However, officials at Government agency Transport Scotland insisted all options would be on the table.