Members of the ASLEF union were planning to walk out for 24 hours due to an ongoing dispute over working hours and pay.
The strike, which would have caused disruptions for millions of passengers on Thursday (October 5), was called off after a breakthrough during a meeting between the union and London Underground.
Finn Brennan, ASLEF organiser on London Underground , confirmed the strike was suspended on Tuesday (October 3).
He said: "I am pleased to say our negotiating team believes we have made sufficient progress in talks at ACAS to recommend to the ASLEF executive committee the strike called for Thursday be suspended.
"We have always been prepared to keep talking to resolve this dispute but ASLEF always has, and always will, insist that management stick to agreements they make with us.
"Our ballot remains live and we will not hesitate to call action in the future if needed to ensure all the commitments made are fully delivered."
Commuters were not the only one to be affected by the tube strike, as thousands of football fans heading to see England play Slovenia at Wembley on Thursday would also have had their journeys disrupted.
Nigel Holness, director of network operations for London Underground, spoke before the strike was called off and said the company was "working closely with unions".
He said: "We are committed to ensuring our employees are able to maintain a good balance between their work and personal lives and we have been working closely with the unions on new ways to achieve this."
The Mayor of London, Sadiq Khan, responded to the news of the strike suspension on Tuesday (October 3).
He said: “I'm pleased that this strike action has been suspended and that discussions can continue without disruption.
"By talking constructively to Transport for London staff and acting on their concerns we've managed to improve the atrocious industrial relations legacy left by the previous mayor.
“This has led to a nearly 60 per cent reduction in the number of days lost to strikes on the underground since I became mayor – which means less disruption and frustration for commuters in London."
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