Footage posted to social media showed the hooded assailants hit the victim in the back of the head outside JD Sports on Argyle Street at the corner of Queen Street.
The 16-year-old victim was treated at Glasgow Royal Infirmary for a head injury following the assault on Thursday evening.
Police are now appealing for witnesses.
Police Scotland said: “I am appealing to anyone in the area who may have seen the men involved before or after the incident to get in touch.
“Also, I would ask anyone who may have captured images or video footage on their mobile phones to contact us.
“If anyone captured footage on dashcam, please get in touch.”
Anyone with information is asked to call police via 101, quoting incident 0387 of Thursday July 1, or call Crimestoppers anonymously on 0800 555 111.