The British Olympic Association (BOA) has now officially told the International Olympic Committee (IOC) that Glasgow would like to stage the event.
The bidding process could cost as much as £2million, but it is claimed the benefits of winning the event could be many millions more.
It is too early for Glasgow City Council to estimate the cost of hosting the games or the financial benefits if the IOC is convinced by the bid.
But television coverage could reach around 250 million people in 160 countries – giving Scotland's and Glasgow's tourism industry priceless exposure.
A council spokesman said the bid cost would be underwritten by the Scottish Government and the city council.
Council leader councillor Gordon Matheson said: "One of the biggest benefits we'll get is the worldwide television coverage that Glasgow will get.
"That's the kind of global TV exposure that money just can't buy and would yet again show that Glasgow is one of the world's leading cities."
One-off major sporting events – such as the Champions League final in 2002 – generate millions of pounds for the city's economy and the council expects that the 2018 Youth Olympics would bring in a substantial amount of cash.
Glasgow's bid is expected to be strong: by 2018 the city will have hosted events for the London 2012 Olympic Games, and the 2014 Commonwealth Games.
Over the coming months, the BOA will work with city officials and the Scottish Government on the submission before the final bid is delivered to the IOC in October.
The winner will be announced next summer.
Councillor Matheson added: "Our submission for the Youth Olympic Games is a strong one, reinforcing our credentials as hosts of world-class sporting events and underlining our continuing determination to ensure Glasgow has an enduring legacy which will benefit the city for generations to come.
"The economic, environmental and social legacy from the Commonwealth Games already being created for Glasgow is making a genuine difference to many people's lives.
"Winning the right to host the 2018 Youth Olympics would allow us to continue to build on that legacy work."