Kjell Lindgren of the Stockholm police said the teen is being held on suspicion of murder, according to Sveriges Radio (SR).
The stabbing occurred at around 11pm last Thursday in the area between the Stockholm Public Library and Rådmansgatan metro near the Stockholm School of Economics.
The victim, a 29-year-old Romanian citizen, was stabbed in the face and throat and died from his injuries at the scene. Ambulance staff made attempts to resuscitate the man without success.
The Romanian embassy has been notified about the incident.
Around ten police units took part in the search for the assailant who was seen fleeing from the scene by several witnesses along Sveavägen. The suspected attacker then turned himself in to Norrmalm police several days later.
It remains unknown if the teen and the victim were acquaintances, but it is believed the two were involved in some kind of altercation in a nearby park before the attack.