The money will help set up a nationwide network of emergency supply centres expected to feed 400,000 Scots over the next five years. The award of £944,708 has been given to the Christian charity the Trussell Trust, which already manages 400 food banks in the UK including 40 in Scotland.
The trust said 71,428 Scots used food banks over the last year, up from 14,318 since 2012/13.
Everyone who turned to them was referred by officials from frontline agencies such as social workers, welfare rights staff and school community liaison officers. Most of those using the banks were in Glasgow, where 9687 people turned to them.
Edinburgh had the second highest number of users with 6707, while in Dundee the number was 5990. Last year the 40 Scots food banks managed by the Trust collected around 691 tonnes of food through donations from churches, schools and supermarket customers.
Maureen McGinn, chairwoman of the Big Lottery Fund, said the award would help some of Scotland's most vulnerable people struggling with hunger, poverty and unemployment. She added: "We are well aware of the current levels of hardship experienced within many of Scotland's communities. It is our mission to support these people through a wide range of projects."
The cash will allow the Trussell Trust to target areas where there are currently no emergency food banks and to employ and train staff to set up new centres. It will also enable existing ones to continue to get support.
Ewan Gurr, Scotland development officer for The Trussell Trust, said: "The massive rise in demand for emergency food relief highlights the extent to which food banks are a lifeline to many Scottish families. The Big Lottery Fund has a tremendous track record of supporting many worthy causes and we are pleased they have sought to support our efforts in Scotland."
Jamie Livingstone, head of Oxfam Scotland, added: "The fact the number of people forced to rely on food banks in Scotland has increased by five times in the past year is deeply worrying. Food banks, and the thousands of people who support them, are doing an incredible job in helping stop people from going hungry, but the truth is that in a country as rich as Scotland food poverty should not exist."
Ailsa Kellett, 48, a former nurse and carer, was among those who turned to a food bank when she found herself unemployed and homeless. She moved to the Western Isles for two temporary jobs, but when these came to an end she could not find work.
The divorced mother-of-two said: "I have paid into the welfare system for years, but when I needed it most, it failed me. I was reduced to mixing flour with water, frying it in oil, coating it in sugar and having that for dinner. That is what austerity does to people like me."
In February this year Glasgow City Mission's food bank ran out of food and had to turn people away as the number of families going there increased following the Christmas and New Year holiday. It later reopened after extra donations of food were received.
The award to the Trussell Trust comes from the Big Lottery Fund's Investing in Communities fund which is aimed at projects that support those communities, individuals and families in greatest need. It has already awarded more than £1m to more than 100 projects through its Support and Connect programme aimed at supporting communities in Scotland to deal with increasing hardship.
At the SNP Conference on Friday, Deputy First Minister Nicola Sturgeon announced a £1m package of support for food banks.
SNP MSP Linda Fabiani, who sits on Holyrood's welfare reform committee, said the new figures showing the huge rise in numbers using food banks were "a disgrace". She added: "It is the grim reality of Westminster's cuts that has seen food bank use increase."
l Separate figures show the proportion of people using credit to pay their rent or mortgage is on the up. A total of 5.5% of Scottish residents, equivalent to more than 290,000 people, said they had turned to a payday loan, credit card or loan to settle their main monthly household bill.
The figure is up from 3% last August. Ian Williams, of Debt Advisory Centre Scotland, which conducted the research, said it was a "real cause for concern".