The Evening Times revealed the plan yesterday, but train users have expressed concerns about the long timeframe for the project and fears over higher ticket prices.
Deputy First Minister Nicola Sturgeon announced the plan, which would see a new line being built.
A £650million programme to electrify the current Glasgow-Edinburgh route is already under way and it is expected to reduce journey times of 50-55 minutes by 10 minutes.
But the new plan is separate. The projects costs or exact details of the route have not yet been revealed.
Ms Sturgeon said it would bring the Scottish rail network "into line with the most forward-thinking transport systems in the world".
We spoke to a number of people at Queen Street Station after the announcement and most agreed the idea was positive.
However, they all expressed concerns that it would mean vastly higher ticket prices and also about the length of time before work is completed.
Among the issues raised was the proposed 2025 completion date.
Martin McDowall, 30, from Dennistoun, commutes to Edinburgh for his job in IT.
He said: "A new line would make a big difference, but with completion being so far away I don't think it means much to commuters today – who knows where we will be in 10-15 years?"
Ronnie Singh, 24, from the South Side, who travels to Edinburgh as part of his job with a law firm, said he thought the idea was "brilliant".
He added: "It is currently about 50 minutes, so if it was quicker, that would be great."
Ms Sturgeon made the announcement as politicians and railway experts gathered in Glasgow for a two-day conference on the benefits of the UK Government's High Speed Rail plan and for the need for Scotland to be included.
High Speed Rail is a proposal for a fast route from London via Birmingham, which would only go as far north as Manchester and Leeds.
But the Scottish Government, with council leaders in Glasgow and Edinburgh, will lobby UK ministers to include Scotland in the High Speed Rail plans.
It is planned for the new Glasgow-Edinburgh route to be open before the London-Birmingham link is complete in 2026.
If the Westminster UK High Speed2 plan is to eventually come to Scotland it will be at 2034 at the earliest. But Ms Sturgeon said Scotland was not able to wait for Westminster to act and that was why the Scottish Government wanted to start on the new Glasgow- Edinburgh 140mph plan.