At the International Olympic Committee (IOC) headquarters in Switzerland, President Jacques Rogge said Glasgow would join Buenos Aires and Medellin on the shortlist for the next stage of the process.
In July, IOC members will choose the winning city.
Glasgow, which is hosting the 2014 Commonwealth Games, was praised by the IOC for hosting international sporting events, while the 2018 Youth Olympic Games (YOG) Working Group report said the bid would build on the success of London 2012.
Up to 3600 athletes aged between 15 and 18 are set to take part in 28 sports at the 12-day 2018 Games.
The YOG committee found that Glasgow's budget was sound and that the bid was "clear and good quality".
Guadalajara in Mexico and Rotterdam in Holland were excluded from the shortlist due to issues with financial guarantees.
The regeneration of an area of Glasgow is being brought forward as part of the bid.
Sighthill, in the north of the city, will be home to the athletes' village if the bid is successful, but work will begin before a city is chosen due to the timescale of the bid.
Lord Coe, chairman of the British Olympic Association, said: "Glasgow cannot only stage a compact, sustainable and financially sound Youth Olympic Games, but take a unique journey in history hand-in-hand with the Olympic movement fuelled by the passion and warmth of Scotland."
Rower Katherine Grainger said Glasgow would be the perfect host. The Olympic gold winner said: "For many young athletes the Youth Olympic Games will be the first step towards competing at the very highest level and it is fantastic to think that they may be taking those steps in Glasgow.
"The city has a proven track record of delivering major international sporting events in world-class facilities in front of passionate crowds."
The bid is being run by the Scottish Government, Glasgow City Council and the BOA.
Scottish sport minister Shona Robison said: "Glasgow 2018 will put the aspirations and talents of young people at the centre of the Games, and my congratulations go to the young people at the heart of the bid."
Glasgow City Council leader Gordon Matheson said: "Glasgow is extremely proud to have been granted the privilege of being shortlisted by the IOC."
Prime Minister David Cameron visited Glasgow last year to back the bid and said he was delighted to see it shortlisted.
He said. "This is fantastic news for Glasgow and a massive vote of confidence in the UK's ability to host major sporting events. When I visited Glasgow last year to back the bid, I was impressed by the commitment and dedication of the team who are working so hard to win the bid."
l Andy Hunt is to step down as chief executive of the British Olympic Association at the end of February. The Chef de Mission for Team GB at the 2012 Games leaves after four years.