The Northern train can be seen split into two parts in this photo taken by passenger Marc Thornton.
Although the locomotive has now been cleared from the tracks, delays are expected to affect services until 8pm tonight.
At one point, a traveller Tweeted a photo of a departure board showing delays to nearly all services listed.
Other passengers described the situation this afternoon as 'chaos' and 'mayhem'.
It is not known how the accident happened, and passengers on the decoupled train are believed to have been evacuated. It had to be moved away from the scene in two parts by engineers.
Network Rail said the 1.25pm Northern Manchester Victoria to Leeds service separated just outside Leeds rail station at 3.15pm today.
Forty passengers were evacuated and had to walk across the tracks to platform seven. The broken down train has been moved to platform 11.
Nobody was injured in the incident.
Platform 11 will be out of use for the rest of the day.
A spokesman for Northern said: “At around 3.10pm this afternoon a train broke down as it approached Leeds station.
“The train, a Class 150, divided on the approach to the station. There were no injuries to any customers or staff and all on board were safely evacuated.
“The Rail Accident Investigation Branch has been informed and Northern is now working to determine exactly what caused the incident.
“Services in and around Leeds have been severely impacted as a result of the incident and are subject to alterations, cancellations and delays.”