The crash, at the junction of Bingley Road and Toller Lane at around 5.30am, has been referred to the police watchdog because an unmarked police vehicle was following the men's BMW.
Four killed in tragic Bradford smashIn a statement, West Yorkshire Police said:
"Police can now confirm that four males who were in a car which was involved in a road traffic collision at 5.30am on Bingley Road at the junction with Toller Lane in Bradford this morning have died.
"The road is currently closed and is likely to remain so throughout most of the day.
"Due to the nature of the incident it has been referred to the Independent Office for Police Conduct."
Residents living close to the scene of the crash reported hearing a "really loud bang" at about 5.30am on Thursday.
Roger Wood, 67, said: "It woke me up really early in the morning, there was this really loud bang down the bottom of the road.
"It wasn't until I woke up properly later in the morning that I found out what had happened, when one of my neighbours said they'd seen on the news that people had died. It's horrendous, horrendous."
Another nearby resident, who did not wish to be named, said that she had long-held concerns about safety on Toller Lane.
The mother-of-two said: "I was horrified when I first heard about it, but I wasn't surprised when I heard that it was Toller Lane where it had happened.
"It's known for being a bit of a speed-trap and there have been accidents down there in the past."
Christine Yates, who lives less than a minute's walk from the crash site, said that the car involved was "smashed up against a tree".
She added: "I knew that it was a very serious incident when I saw the number of emergency service vehicles that were there on the scene, as there were an awful lot of them".
Salim Rahman said that he too was awoken by the sound of the car crashing into a tree.
The 69-year-old said: "I have been living on Toller Lane for 33 years and there are always cars coming up here too quickly. It's not unusual to hear sirens and police chasing people."
Describing the victims as "youngsters", he added: "It's incredibly sad to hear about it, your heart goes out to their parents."