The accident happened on the A705 near Seafield, West Lothian, at around 11.05am yesterday when the Vauxhall Astra came off the road.
Driver Louis Kefferty, 20, and his 18-year-old passenger were taken to Edinburgh Royal Infirmary for treatment to serious injuries.
Mr Kefferty died late last night, police said.
The 18-year-old remains in hospital but his injuries are not thought to be life-threatening.
The road was closed for five hours while officers examined the scene and they are appealing for any witnesses.
Sergeant Brian Jones said: "This tragic collision appears to have involved only one car. However, I am appealing to anyone who saw the collision or was driving on this road around this time and has any information which can assist us to call Police Scotland on 101 or provide the information through Crimestoppers on 0800 555 111."
Meanwhile, two people are being treated in hospital after a head-on crash in Aberdeenshire.
Emergency services were called to the scene on the A96 Huntly to Glens of Foudland road at around 12.10pm yesterday.
The collision involved a silver BMW 3 series being driven east towards Inverurie by a 65-year-old woman and a black Audi A3 being driven west by a 58-year-old man. There were no passengers in either vehicle.
The woman was airlifted to Aberdeen Royal Infirmary by an RAF Lossiemouth search and rescue helicopter and remains in a serious condition.
The man was taken to the same hospital by ambulance and is being treated for a broken collarbone and other minor injuries.
Inspector Ewan Innes said: "Our inquiries are at an early stage and at this time it is too early to speculate as to the exact cause of the collision.
"I am aware that there were several vehicles travelling on this section of the road at the time, and I would ask anyone who may have witnessed the collision, or who has any information relating to this collision that has not yet come forward to please do so in order that we can speak to them."