The move starts on January 31 as part of an SNP Budget deal with the Scottish Greens.
Ministers had planned to increase the eligible age from the under 16s to the under 19s, which was delayed by the Covid pandemic.
The Scottish Government’s Transport Scotland agency estimated some 930,000 people would benefit.
It said the necessary legislative changes would be introduced to the Scottish Parliament this summer.
Around one third of people in Scotland already qualify for free bus travel, such as the over-60s and people with disabilities since 2006.
Mr Dey said: “It’s crucial to embed more sustainable travel behaviour from a young age if we are to achieve our world-leading goal of reducing the number of kilometres travelled by car by 20 per cent by 2030 and reaching net zero emissions by 2045.
“We also know that young people have been disproportionately impacted as a result of the Covid-19 pandemic, so it’s never been more important that we support them to achieve their fullest potential.
"Reducing barriers created by transport costs is one really positive action we can take.”
The Scottish Greens said launch of the scheme had been delayed by Covid-19 and a shortage of silicone, which the party said was vital in the manufacture of the concessionary cards.
Co-leader Patrick Harvie said: “Free bus travel for young people is not only a transformational policy in terms of family budgets and opening up opportunities for young people, it can help shift people out of car use and help tackle the climate emergency.
“What’s more, as we recover from the pandemic, this policy will be vital in encouraging people back onto public transport safely to ensure we have a green recovery.
"The Scottish Greens believe public transport should be free at the point of use and serve all our communities, and January will see a major step forward to this aim.”
However, Scottish Labour transport spokesperson Neil Bibby said: “It's been over 500 days since the deal to extend concessionary travel was done.
"Any progress is welcome but the truth is this is slow progress in the face of a climate emergency and steep decline in bus services, all compounded by the Covid crisis.
"Across Scotland, routes have been slashed and passenger numbers are plummeting.
"Scotland’s broken bus market is failing our young people.
"Not only should government make bus travel affordable, it should also make sure there is a reliable bus network for young people to use these new passes on.”
"Labour supports extending free bus travel to all under-25s and concerted action to build an affordable, integrated modern public transport network that works for all of us."
Kirsten Urquhart, interim chief executive of Young Scot, said: “Young people often tell us about the positive impact free travel would have on their lives.
"For some, it'll help them to travel to work or take part in learning.
"For others, it'll improve their well being by making it easier to socialise and to meet with their friends and family.”