Oliver Pryde,18, died when a car collided with him as he crossed Penistone Road, in Kirkburton, Huddersfield at around 12.20am on Monday, July 12.
Mr Pryde, who was studying mathematics at the University of Huddersfield, was originally from Cumbria.
He previously attended Netherhall School in Cumbria.
In a statement posted on the school's Facebook page, the school said: "It is with the greatest sadness that Netherhall School writes to inform you of the tragic and unexpected death of former sixth form student Oliver Pryde.
"Oliver was pursuing his lifelong dream and career ambition, successfully studying mathematics at Huddersfield University.
"Oliver left Netherhall School last summer; he was a superb student, impeccable young man, a joy to be around, loved and respected by all and a great credit to his family, many friends, teachers and fellow students.
In a statement, his family said: “Oliver will be incredibly missed by family and friends and request privacy at this time.”
West Yorkshire Police have renewed their appeal for information following Mr Pryde's death and are appealing for witnesses who may have seen the crash.
Two men in their thirties have been arrested on suspicion of causing death by dangerous driving and a number of other offences.
Both have been bailed pending further enquiries.
Anyone with information is urged to contact West Yorkshire Police's major collision enquiry team on 101 quoting log 0075 of July 12.