Eoin Farrell and his friend died in the single-car collision in Rostrevor just before midnight on Monday. Another of their friends was critically injured.
They all attended courses at the Southern Regional College in Armagh.
Eoin's father, Gerard Farrell, paid tribute to all three, adding he had lost a "great son" who "loved life".
He described the fatal crash as an "awful tragedy" which had come as a terrible shock to their family.
The car his son was travelling in struck the wall of a house and crashed into a field on the Kilbroney Road.
The other teenager who died at the scene has been named locally as James Miskelly, from Mayobridge, County Down.
Eoin, who was 17, lived at his parents' home in Rostrevor.  In addition to attending to studying motor vehicle maintenance at the college's Armagh campus, he worked as a trainee lorry mechanic in Newry, County Down.
"Eoin was just fun-loving, easy-going, loved working," Mr Farrell told the BBC.
"He came home in the evenings, he was only in the house five minutes and he was away with the other boys... working at cars or doing a bit of farming or fishing, always on the go, always enjoying life, always with his cheeky smile.
"There wasn't a bad bone in him.  Great son, just a great, great son. We all loved him."
He described how he was woken in the early hours of Tuesday morning by news of his son's death.
"It was an awful shock at four o'clock yesterday morning. I was texting him and ringing him to see where he was, was he coming home, because he was going to Tech on Tuesday morning with James in Armagh.
"The week before he stayed in James' house and I thought that's where he was going. I rang him at five to twelve, and his phone was flat since eight o'clock.  But then we got the knock at the door at five to four, and we knew something wasn't right."
Mr Farrell also expressed his sympathy to the families of the other victims killed and injured in the collision and said his "thoughts and prayers" were with them.
"An awful tragedy, I wouldn't wish it on anybody," he said.
The chief executive of the Southern Regional College, Brian Doran, said it was "absolutely tragic news" that had left staff and fellow students in "a state of shock".
"Our heartfelt sympathies go out to the Miskelly and Farrell families at this time," Mr Doran said.
"Two young men cut down in the prime of their lives, it's been an absolute shock to everyone here at the college and, most notably, to their classmates."
He added: "The students, as you will appreciate were in a state of shock and we've been working with the students to provide them with support."
The father of one of the two teenagers killed in a County Down car crash has said they lived life to the full and had become inseparable friends.