The three cities will now go forward to be assessed by the International Olympic Committee evaluation commission in April before the final vote in July.
Dancers held a flash mob in Glasgow's Central Station to celebrate the city being shortlisted for the Youth Games. Watch the video below.
Video by Mark Gibson
Guadalajara in Mexico and Rotterdam were both ruled out of the race by the IOC’s executive board which met in Switzerland today.
Glasgow became the UK’s candidate city for the 2018 Games in February last year.
The first summer Games, which were held in Singapore in 2010, attracted a worldwide television audience of more than 247million people.
City council leader Gordon Matheson said: “We will continue to work hard to show how this city can be a valuable partner of the Olympic Movement to better the lives of young people both here and across the globe.”