The body of Ben McLean, 19, was discovered in the garden of a tenement in West Preston Street on Friday morning.
It is understood he had been at a party in the block and fell from the window while others were sleeping.
Mr McLean is understood to have been a second-year student at Edinburgh University’s Medical School and was described by his secondary school as a “role model”.
In a statement, his heartbroken family described him as “talented” and “generous”.
“We are completely devastated at the loss of our talented and much loved son,” it read.
“Ben was gentle and generous, with a great sense of humour and a determination to be the best he could be. Words cannot describe our grief.
“We would like to thank everyone for their kind messages and the support that we have received, and also request that our privacy be respected at this incredibly difficult time.”
Police Scotland said inquiries into the full circumstances surrounding the death of Mr McLean, originally from East Renfrewshire, are ongoing.
A 19-year-old man has been charged in connection with drugs supply.
His former high school, St Luke’s High in Barrhead, released a poignant tribute describing him as an “outstanding student” who was “highly regarded” by his teachers and peers.
In a statement, the school said: “We are devastated to hear about the tragic death of one of our former pupils and extend our heartfelt thoughts and prayers to his family at this very painful time.
“Ben was an outstanding student both in terms of his academic attainment and personal qualities.
“Ben enjoyed excellent relationships with his peer group and his teachers and was a role model to younger students through his responsibilities as a senior prefect, S6 buddy and as a peer educator within the faculty of science.
“He spent much of his time in science, such was his commitment to achieving his academic goals and working towards a career in medicine, he was very highly regarded of by his teachers and the technicians with whom he worked most closely.
“Ben was always willing to give of his time to help others and without doubt would have enjoyed tremendous success in the field of medicine.
“Ben will be very sorely missed by all at St Luke’s and we will always remember him and his family in our thoughts and prayers.”
The News previously told how Mr McLean’s girlfriend, Paige Watson, had revealed that her friend Kyle Doherty – a promising footballer – died earlier this month after falling down a utility shaft during Hogmanay celebrations.
Dance music fan Kyle’s body was discovered in Manchester on New Year’s Day.
The 19-year-old, who played for Stenhousemuir’s under-20s team, was laid to rest on Thursday, just hours before Ben suffered a similar death.