Councillor Yvonne Davies was suspended by the Labour Party over the allegations.
In a Sandwell Council Cabinet meeting this afternoon she stood down as council leader, aiming a broadside at “the white male old guard” who she said sought “only to preserve their own power base for its own sake”.
Councillor Davies was under investigation by Labour after the head office received complaints relating to a series of tweets she posted in 2017 and 2018.
Labour sources confirmed earlier today that she had been suspended pending the outcome of the investigation.
Councillor Davies then announced her resignation as the leader of the council in an 18-minute statement during a meeting of the cabinet today.
Deputy leader Maria Crompton will lead the council temporarily.
Councillor Davies, who represents Langley and was elected leader in May 2019, led a Labour group Zoom meeting last night.
Sources say the issue was not mentioned during the meeting.
One of the tweets posted by Councillor Davies features a link to a petition calling for a parliamentary debate over whether Israel has "improper influence" over British politics.
Another suggests "Israel's hand" was behind criticism of Jeremy Corbyn, and a further tweet features a link to an article claiming "the Jewish establishment's 'War Against Corbyn' risks bringing real antisemitism to Britain".
The article is described by Councillor Davies as "a real breath of fresh air".
In an interview with the Express & Star last August when she became Sandwell Council leader, Councillor Davies said she was on a mission to bring “justice and fairness” to a borough that has spent years dogged by scandal and in-fighting among members of its Labour group.
Councillor makes robust statement
Councillor Davies told the cabinet: "I'm not anti-Semitic. I'm horrified I might even be considered so to be.
"Equally, I am as aware as our party leader, of the risks of unconscious bias and the dangers of perpetuating negative tropes.
"If I had been asked about this I could've apologised for my historic misjudged. Maybe it's because I'm a woman, possibly it's because I'm a strong woman, or maybe other factors have been at play about the approach I've tried to bring to the running of the council.
"I said that as public servants we answer to the people of this borough and they should expect that we will, at all times, conduct ourselves with the utmost integrity and uphold the highest standards in public life.
"I commented, in the recent past, that we had fallen well short in this regard. Since then I have worked as hard as I can to deliver on that promise."
She added: "Is this really about anti-Semitism? Or is it about a cover-up of some disturbing truths that are shortly to come into the public domain?
"This is more about powerful self-interest seeking to avoid proper scrutiny.
"Proper accountability for those who have fallen disgracefully short.
"Is it the white male old guard who are at the heart of this shocking behaviour in the past? Who did leak this information to the press and whipped up a campaign to remove me from office?
"What was the role of the local MP in all of this? Ask yourselves 'how far does the collusion and malign intent reach up into the Labour Party hierarchy?"
She added the alleged corruption of the council needed to be "brought out" into the light of day.
"I won't be here when this is done. I am resigning my position as leader but the questions and the choices will remain for the Labour Party, for the Sandwell Labour Group and for the people of this fine borough.
"Right now the choice is pretty stark. There is a group of old white men who want to go back, back to the vile bating, the poisonous leaking, and the misuse of public funds for political retribution.
"Millions of pounds, and I do mean millions of pounds, of public funds have been spent with little regard to the public purse.
"The white male, old guard will play lip service to equality and black lives matter but who will seek only to preserve their own power base for its own sake.
"Or the council can embrace a new future where its elected representatives are humble.
"Humble in their service to the public where they absolutely respect they serve only in the interests of the people of Sandwell. Where one gives real meaning to the fight against inequality."
"People in this borough absolutely deserve the best council, led by the best councillors, driven by the right values.
"This self-serving, political malignancy and this interference in local leadership by outside party interests serves only to undermine confidence in this council's ability to serve its people well.
"But that future is for others. I won't be here to lead you. I've got other things to do; I've got places to go and people to see. But the questions genuinely really need to be answered long after my leadership is over."
Former Dudley North MP Ian Austin previously described the tweets as "completely unacceptable", while Warley Labour MP John Spellar called on Councillor Davies to apologise.
Councillor Davies became the third leader for Sandwell Council in a matter of months after Steve Trow stepped down in the immediate aftermath of the local elections in 2019.
He in turn had replaced Steve Eling, who was among several borough councillors to be suspended or thrown out of the party by Labour’s National Executive Committee.
In January, former Labour deputy leader Tom Watson called for Councillor Davies to stand down, saying she lacked the skill and "humility" to guide the authority away from its scandal-riddled past.
New Labour leader Sir Keir Starmer apologised to the Jewish community for anti-Semitism in the party and promised to “tear out this poison by its roots” when he was elected in April.
He sacked Rebecca Long-Bailey from the shadow cabinet after the MP shared an article online containing an allegedly anti-Semitic conspiracy theory.
The Labour Party has been contacted for a comment.