Corbyn today said he wanted to see nuclear defence jobs at the Faslane naval base cut and transferred instead to other forms of "high-value engineering".
He told the BBC: "I think Trident should go. I do not believe that it is a form of defence.
"I do not believe it is something that anyone in their proper mind would ever want to use, so I ask the question is it really sensible to commit such a vast proportion of our assets - £100bn over 25 years - to this when we could be spending it on developing our industrial infrastructure?"
The Islington MP added: "In the House of Commons, I was chair of the CND [Campaign for Nuclear Disarmament] group and one of the vice-chairs is from the SNP and yes we will be voting with them on this, or they will be voting with us, whichever way you want to put it."
Labour is set to hold an open debate on the controversial nuclear arms system at its conference this weekend, and Scottish-wing leader Kezia Dugdale has said the winning argument will become the position of the her national party.
SNP MPs welcomed Corbyn's comments, but warned that "deep divisions" within Labour on the issue would emerge at the party upcoming Autumn event, due to be held in Brighton.
Defence spokesperson Brendan O'Hara said: "The pressure will be on the Labour Party to clarify their position and whether or not they support their leader, and whether they will work with the SNP in opposing spending £100 billion on Trident's replacement.
"Labour have an opportunity to join a progressive alliance against the immoral, obscene and completely redundant weapons of mass destruction that Westminster continues to dump on the Clyde."
He added: "If Corbyn and Labour have any hope of being treated seriously by the vast majority of voters in Scotland, then he must get party support in his commitment to backing the SNP's plan to scrap the replacement of Trident.
"Indeed, if he cannot then many more people in Scotland are likely to conclude that independence is the only way to ensure getting rid of Trident.
"The people of Scotland sent a clear message to Westminster in May; we simply will not accept a new generation of these weapons.''
Scottish political leaders last month accused George Osborne of "pre-empting" the vote on the future of nuclear weapons by preparing the Faslane naval base for the renewal of Trident.
It came after the Chancellor announced a £500 million investment in the Clyde base that was designed ''partly to ready Faslane for Trident's replacement''.