The pair were said to have fallen on to tracks at Ealing Broadway at 18:10 BST on Tuesday.
Police said they were treating the deaths as "unexplained" and had not yet identied the victims.
Heathrow Express services were suspended, while First Great Western said there were delays of up to 90 minutes to and from Paddington.
British Transport Police said: "We were called at 6.10pm to Ealing Broadway station following reports that someone had been hit by a train.
"We attended along with the Metropolitan Police, London Ambulance Service and London Fire Brigade and discovered two people had been struck and killed by the train.
"We're still working to determine the identities of the deceased or how they came to actually be on the tracks."
The force said the train was London-bound.
Last night, commuters took to Twitter to express their concern.
Girl_about_town tweeted: "Just changed at Ealing Broadway. Rammed with firemen and policemen. Sadly two deaths, apparently."
Thomas Clements wrote: "Forensics still on the track at Ealing Broadway. Just witnessed an utterly horrific scene. Feel for the people who have to deal with it now."
Tom Kimber tweeted: "So the train I'm on has hit two people at Ealing Broadway. A sad business."
A spokesman for First Great Western said: "We are doing all we can to help the police with their investigation into this terrible incident."

The economy grew at an annualised pace of 2.1% in the fourth quarter of the year, the Commerce Department said, up from an earlier estimate of 1.9%.
But the data had little impact on shares, with the Dow Jones up 20.23 points, or 0.1%, at 20,679.55.
The S&P 500 edged up 2.17 points to 2,363.30 while the Nasdaq added 5.63 points to 5,903.18.
The biggest faller in the Nasdaq was sportswear maker Lululemon Athletica, which plunged by nearly a quarter after it warned that sales were likely to fall.
The company said it expected same-store sales to fall in the first quarter of the year, the first decline since 2009.
Shares in ConocoPhillips jumped nearly 6% after the energy company announced it was selling oil sands and western Canadian natural gas assets to Cenovus Energy for 17.7 billion Canadian dollars ($13.3bn; Â£10.6bn).
ConocoPhillips is not the first oil major to scale back its operations in the region, with both Royal Dutch Shell and Marathon Oil also having sold oil sands assets.
The high costs of extraction have made it hard for companies to make profits with oil prices remaining low.
Two people, one believed to be a child, died when they were struck by a First Great Western train in west London.
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US stocks remained unmoved in early trade, despite an upward revision to the growth rate at the end of 2016.