Speaking in Perth, Mr Ludlam said it was brought to his attention last week that unbeknown to him he held both Australian and New Zealand citizenship.
"It was brought to our attention a week ago while I was still overseas by someone who had done the digging, for whatever reason," he said.
"It took a couple of days to confirm with the New Zealand high commission that that was the case."
It is understood it was not a journalist who pursued the matter of Mr Ludlam's dual citizenship.
The outgoing senator said the decision to relinquish his leadership would be effective immediately.
"I could have dug my heels in. But it creates a messy and protracted dispute. That section of the constitution is crystal clear and it has been tested before by others.
"It is not something that I particularly want to put myself, my staff or my party through. This is probably a cleaner way to just make a break."
In a statement, Mr Ludlam apologised for the bungle and thanked those who had supported him throughout his near-decade long run as Western Australia’s Greens senator, after he was first elected in November 2007.
"I apologise unreservedly for this mistake. This was my error, something I should have checked when I first nominated for preselection in 2006," Mr Ludlam said.
"I am personally devastated to learn that an avoidable oversight a decade ago compels me to leave my colleagues, supporters and my wonderful team."
Greens leader Richard Di Natale commended Mr Ludlam for his “absolute integrity” over the matter, and praised his work while in office.
“It's been devastating for our parliamentary team to learn this news,” Mr Di Natale said.
“If you want to know what kind of person Scott is, you need to look no further than Scott’s announcement today.
“Scott’s decision shows his absolute integrity and character. This is news Scott has just learned, and upon hearing it, he’s taken action immediately.
“As a Senator, Scott has been fearless. Just a few days ago, he was at the UN for the historic vote supporting a treaty to ban nuclear weapons, when Malcolm Turnbull and Julie Bishop refused to give Australia a seat at that table.”
Mr Ludlam, who first stepped into politics after joining the anti-nuclear movement in the late nineties, recently attended international negotiations in New York that sought to bring an end to weapons of mass destruction.
In a landmark decision, more than 120 countries last week approved a treaty to ban nuclear weapons at a UN meeting in which Australia chose not to be involved.
“The Australian role has been disgraceful,” Mr Ludlam told the ABC’s "Lateline" program in July.
“Australian diplomats were instructed, first under Prime Minister Abbott and then Prime Minister Turnbull, to try and obstruct or break up the talks, try to prevent this process from happening at all. Now this process is underway.”
Mr Ludlam, 47, emigrated to Australia with his family before he turned nine and claimed he believed his New Zealand citizenship ceased after he was naturalised in his mid-teens.
Mr Ludlam’s replacement is expected to be announced within weeks.
