A coded warning led police to a package on the line near Ealing Broadway tube station and they sealed off the area and carried out a controlled explosion.
It is understood that the warning was relayed to London Transport Police by a security agency in Northern Ireland.
Thousands of rail commuters in London and other parts of the country have been severely affected, as Ealing Broadway and other key London tube and main line stations have been closed.
Victoria main line, underground and bus stations have been sealed off, as well as Paddington main line and Westminster Tube station.
Police say they received a coded warning which led them to the device, found near a bridge by the railway track close to Ealing Broadway tube station.
They say the surrounding area was immediately sealed off after receiving the bomb threat at 0600 BST.
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A controlled explosion of a small package was carried out at about 1030 BST.
Serious incident
"This is a particularly serious incident and we are treating it as very significant," said Superintendent Tony Thompson.
He said there was no damage was caused to the rail track, but the armed forces were now involved in the security operation, which could cause disruption for several hours.
Commuter trains and services to and from the west of England, South Wales and the Heathrow Express are delayed.
Paddington Station is closed while the Piccadilly, Central and District lines in the area are also hit, London Underground said.
The start of the final day of evidence in the Paddington rail crash inquiry has been delayed because a witness and other interested parties were caught up in the chaos
A spokesman for British Transport Police urged commuters to be patient, although the disruption is expected to last most of the morning.
'Out of our hands'
London-bound Great Western passengers had to take South West Trains services from Reading into London's Waterloo station. Heathrow Express services were suspended.
London Underground described disruption to morning rush hour services as "severe".
Passengers trying to get to Heathrow were further hit by suspension of the Piccadilly Tube line between Acton Town and Rayners Lane, west London.
District line services between Acton Town and Ealing Broadway and services on the Central line between North Acton and Ealing Broadway were also suspended.
A spokesman for First Great Western said its services were stopping at Swindon and Reading and were not expected to be running again before midday at the earliest.
"It is out of our hands as to when the line will re-open," he added.