The Olympics-themed parade runs from Piccadilly to Trafalgar Square where there is live music.
High-jumper Deirdre Ryan and boxer Kenneth Egan, who have qualified for the Games, are among those joining.
There are 220,488 Irish people living in London according to the last census.
Mayor of London Boris Johnson said: 'I'm delighted to once again be backing London's St Patrick's Day celebrations.
"That they are amongst the biggest outside Ireland reflects the longstanding contribution of many generations of Irish people to London life."
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The plaque at number 16 Cowley Street in Westminster marks the brown brick Georgian townhouse where Sir John lived for 31 years.
A man reportedly armed with several knives has been arrested in Whitehall on suspicion of planning a terror attack, police have said.
Metropolitan Police officer, Tom Harrison, has been crawling the course since the race began on Sunday morning.