LNER said due to the severity of the disruption and the number of cancellations, customers were advised to defer travel and use their tickets for services later on or on Monday.
It said passengers would be able to use their tickets with other train companies at no extra cost.
Northern said none of its services were currently running through Leeds while TransPennine Express said lines between Manchester Victoria and York via Leeds had been closed.
Both train operators said they did not have rail replacement transport in place.
CrossCountry said there was a “limited road transport” in place between York and Leeds.
Network Rail said the signalling failure was a result of a defective cable, which affected several platforms at Leeds Station from about 10:50.
A spokesperson said: “Engineers attended site and restored power by 13:20. Some services were cancelled or delayed, and passengers are advised to continue checking before they travel.
“We apologise for the disruption and thank passengers for their patience.”
