The Deputy First Minister defended the ambitious project as achievable and affordable within the time scale set out.
Earlier this month the Evening Times revealed the plans for a high-speed rail line between the two cities, capable of reducing the journey to under half an hour.
The new route, with a new station in Glasgow, capable of linking to the London to Manchester and Leeds line, is the Scottish Government's plan to ensure Scotland is not isolated from new, high-speed routes down south.
The route is proposed to be complete at least ten years before the earliest date the UK Government's High Speed2 line could come to Scotland and before the London to Birmingham route is complete.
The UK line is planned in phases, with building heading north from London to Birmingham, then a line to Manchester in the west and Leeds in the east. If Scotland is included in a later phase it would be 2034 at the earliest, before the lines linked up.
Annabel Goldie, former Scots Tory leader, asked what the budget was and if a cost benefits analysis had been done.
She was sceptical of the benefits and suggested while "ambitious and exciting" it could be "pie in the sky" and asked if a previous estimate of £7 billion made in 2007 was still the relevant cost.
Ms Sturgeon, who revealed the initial plans at Glasgow Central Station, said the overall benefits had to also include Scotland being linked to the UK High Speed Rail route.
She said: "This is exciting and ambitious and I am pleased the Scottish Government is committed to it.
"It is not pie in the sky. Our position is formed by partnership working with local authorities, Regional Transport Partnerships, trade unions and business groups.
"Their recommendations indicate economic benefits.
"It is feasible by 2024 that we can achieve sub 30-minute journeys."
She said the most recent costs estimate was between £8bn and £9bn, but said that was not what the final bill would be, as work on detailed planning and deciding the route was still to be done.
She added: "We need to look at the economic benefits that is estimated to flow from High Speed Rail, not just between Glasgow and Edinburgh, but from the UK route."