The 472 to 117 vote in the House of Commons last evening marked the first major victory for Theresa May as Prime Minister.
It had been called by her predecessor, David Cameron, who this time sat on the backbenches.
May told MPs that it would be "an act of gross irresponsibility" for the UK to scrap itsnuclear weapons.
She was challenged by the Scottish National Party's George Kerevan, who asked, "Are you prepared to authorise a nuclear strike that could kill hundreds of thousands of men, women and children?". May replied with one word, "Yes".
The Trident system was originally bought in the early 1980s from the US by then Prime Minister Margaret Thatcher as a last-ditch defence in case the armies of the former Warsaw Pact, which was disbanded in 1989, overran Europe.
According to UK government documents, since 1969 British submarines carrying nuclear weapons have always been on patrol, gliding silently beneath the waves somewhere in the world's oceans.
The submarines carry up to eight Trident missiles. Each can be fitted with a number of warheads, which can be directed at different targets.
Each of the four submarines carries a sealed "letter of last resort" in the prime minister's hand, containing instructions to follow if the UK has been devastated by a nuclear strike.
UK Defence Secretary Michael Fallon told MPs nuclear threats were growing around the world and Trident "puts doubts in the minds of our adversaries".
The vote widened the crisis for Corbyn, who is facing a leadership challenge from within his own shadow cabinet.
Although Labour MPs were given a free vote, many used the occasion to attack Corbyn, who is a longstanding opponent of nuclear weapons.
