Enda Dolan, 18, from County Tyrone, was in his first term at Queen's University when he was struck by a van on Belfast's Malone Road in October 2014.
David Stewart, 31, of Gray's Park Avenue, admitted a series of charges linked to the teenager's death.
He was sentenced to seven years - three-and-a-half years in prison and the same on licence - last April.
During his trial, the court heard that Stewart, who had consumed drink and drugs before driving his van, drove with the teenager on the roof of his van for about 800 yards before he stopped.
The court was told that the 13 drinks Stewart consumed included six pints of beer and  four Jagerbombs - a mix of a spirit and an energy drink.
Traces of drugs, including cocaine, were also found in his system.
On Monday, following an appeal, the Lord Chief Justice Sir Declan Morgan increased the time Stewart would spend in prison by one year.
Making the ruling, he said: "Nothing this court can do can turn the clock back.
"What happened was senseless needless and entirely avoidable."
A drunk driver who knocked down and killed a student has had his sentenced increased by one year.