The fire, which broke out on Wednesday afternoon, also had an impact on a stretch of the London Overground line between Euston and Harrow & Wealdstone.
Commuters across the country are facing major disruption after a fire closed one of London's busiest transport terminals.
"Network Rail has engineers on site trying to restore services as soon as possible".
Signalling equipment was damaged in the blaze, temporarily cutting Euston's power supply and leading to its evacuation, Network Rail said.
To make matters worse, the Circle Line of the London Underground was closed and other services disrupted because of a signal failure at Earl's Court.
London Midland say train services to and from London Euston have been restored following yesterday's fire.
Extra passengers could be on Aylesbury-bound rail services this evening, after London Euston Station had to be evacuated.
"Engineers are preparing to work through the night to install 100 metres of 11,000-volt power cables, with the aim of getting services back to normal [on Thursday] morning", it added.
"Customers are able to use alternative routes where available but are advised to check before travelling".
Virgin Trains announced that all services would be running this morning as normal, but some could be very busy.
According to the Office of Rail and Road, Euston is the fifth busiest station in Britain with 41.7 million people passing through the gates past year.
A Virgin Trains spokesman said: "Tickets will be accepted for travel or a full refund offered".