High speed rail could be built from the north in an independent Scotland instead of waiting "decades" for it to spread from the south, he told an audience in Carlisle during a speech in which he said the two countries would remain "close friends and neighbours".
Mr Salmond said the UK's current plans for high speed rail "lack high ambition" for Scotland and the north.
He also said an independent Scotland would be an "economic counterweight" to London and the south-east, with people in the north of England still able to work and trade in an independent Scotland without changing currency.
Speaking to business leaders, he said: "Scottish independence would not change many aspects of the day to day life of other countries within the UK.
"Carlisle would still have strong economic links with Scotland, and as a senior UK Government minister revealed to the Guardian just a few weeks ago, "of course there would be a currency union".
He confirmed a feasibility study would be set up to examine the options of creating high speed rail links from Scotland.
Mr Salmond said: "We are already working with the UK Government to prepare joint plans for high speed rail links between England and Scotland. Initial findings from this review are due in the summer. And we are taking the initiative within Scotland - detailed planning is being undertaken for a high speed service between Edinburgh and Glasgow, which could link to high speed lines from England. The business case for that Edinburgh to Glasgow link will be sent to Scottish ministers in just a few weeks' time.
"An independent Scotland could do much more. Rather than paying our share of the borrowing costs for high speed rail, as we wait decades for it to spread up from the south, we can use that money to build high speed rail from the north instead.
"It's time to take positive action. I can confirm today that the Scottish Government will build on the joint work we are undertaking with the UK Government. We will establish a feasibility study to explore in detail the options for building high speed rail from Scotland to England. In doing so, we will work closely with partners across the UK, especially in the north of England. Of course we can't determine the route, until we undertake the feasibility study. But it is a statement of intent. "
Mr Salmond said a vision of the border areas as hubs being at the centre of trade between different parts of the UK required the transport connectivity to link Scotland and the north of England more effectively together.
He said: "The UK's current plans for high speed rail lack high ambition - for Scotland and for the north. They also lack speed - they may not reach Manchester and Leeds until 2032. And Carlisle? Well maybe, to quote Burns, when the rocks melt wi' the sun."
Willie Rennie, leader of the Scottish Liberal Democrats said high speed rail was an argument for "working together".
He said: "Alex Salmond has identified another positive reason for someone to stay in the United Kingdom. By removing Scotland from the UK he removes Scotland of any influence over acceleration of high speed rail.
"High speed rail is not an argument for independence, it's an argument for working together. If he was being straight with the people of Carlisle Alex Salmond would have told them that his economic policies would have a detrimental effect on their economy. It would take more than a fast train to save the damage caused by his race to the bottom on corporation tax."
The First Minister confirmed during his speech that the Scottish Government intends to host a series of forums on economic co-operation with the north of England in the event of a Yes vote in the referendum, inviting representatives from local authorities and business organisations to participate.
He also told those gathered: "You will remain Scotland's closest friends, as well as our closest neighbours."
In his message, which came on St George's Day, the SNP leader added: " People would still live in Annan and work in Carlisle, or live in Penrith and work in Lockerbie. Friends and family would continue to visit each other. We would still watch many of the same television programmes. People from Scotland and England would still celebrate personal unions - by getting married in Carlisle Cathedral, like Sir Walter Scott and Charlotte Carpenter, or perhaps by going to Gretna instead."
The Prime Minister also issued a plea today for the people of Scotland to remain united with England in the "world's greatest family of nations".
David Cameron said it was possible to be proud of the individual nations in the United Kingdom while remaining committed to the union.
He said the UK was a "global success story" and "no matter how great we are alone, we will always be greater together".