The bid, seen as another legacy of the 2014 Glasgow Commonwealth Games, is expected to clear its final hurdle with approval for its budget next week.
The Scottish Government is funding 70% of the costs, with Glasgow City Council coming up with the remainder.
Glasgow will compete against five other cities from across the globe: Poznan in Poland, the Dutch port of Rotterdam, Guadalajara in Mexico, Medellin in Colombia, and the Argentinian capital Buenos Aires. The winning candidate will be announced in July next year.
The bid aims to rely mainly on sports venues being developed and improved for the 2014 Games, as well as rowing and canoeing facilities at Strathclyde Park in North Lanarkshire and the Scottish National Sailing Centre at Largs, North Ayrshire.
The only new build plans are for a BMX track and a diving pool as an extension to Tollcross, in the east end.
Currently there is no BMX track suitable for major events in Scotland, while there is also no training or competition standard diving pool in the west of the country.
The present favoured location for the BMX track is Alexendra Park, in Dennistoun.
A new Games Village would be built at Sighthill, which was previously a frontrunning location for the 2014 accommodation, meeting all the requirements of the International Olympic Committee.
It is funded separately and as one of the key regeneration areas in the city will go ahead regardless of whether the bid is successful.
Organisers want Glasgow to follow on from the success of the 2010 Youth Olympics in Singapore, where the sale of 230,000 tickets and merchandising netted the city £6m.
It also drew 38,000 international visitors and worldwide media attention. It was broadcast to an estimated worldwide audience of 247 million.
If successful, Glasgow would also join a powerful roster of Olympic cities, including Sochi in Russia, Rio in Brazil, and Nanjing in China, countries that account for 40% of the world's population and more than 25% of global gross domestic product.
In all, the estimated Games budget at 2018 prices is £203.8m and with a contingency provision of £30.5m added, this amounts to £234.3m.
Glasgow's contribution would be £70.2m spread over 2013 to 2019, with the majority of spend expected in the later years. The Scottish Government would be providing the contingency cash.
Council leader Gordon Matheson said: "This is a unique opportunity for the UK to continue its Olympic journey and continue to inspire a generation of young people in the wake of London 2012.
"Winning the bid would not only further enhance our reputation on the world stage but also continue to sustain and create jobs in our tourism, creative, event and service industries which are so vital to the city's economy."
Commonwealth Games minister Shona Robison said: "Hosting the Youth Olympic Games in 2018 is an exciting prospect for Glasgow and Scotland and will build on the sporting legacy from the 2014 Commonwealth Games."
However, the city's sole Tory councillor, David Meikle, raised concerns over the scale of the outlay. He said: "We need to ensure there's a full discussion, that this proposal is fully examined and the outlay consulted on before we sign up to this."
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