The full page advert, published in The Guardian on Wednesday, criticises Mr Corbyn for a “toxic culture you have allowed to divide our movement”, saying it has prompted the resignation of “thousands” of members.
The party, it says, is no longer a “safe place” for its members and supporters.
“We are saying you are accountable as Leader for allowing anti-Semitism to grow in our party and presiding over the most shaming period in Labour’s history,” it adds.
The advert is supported by a total of 67 Labour members of the House of Lords, including Peter Hain, Peter Mandelson and Robert Winston, and comes after a damning report by BBC’s Panorama programme into the party’s handling of allegations of anti-Semitism.
Labour Baroness Hilary Armstrong told ITV News it is taking too long for the party leadership to get a grip on the issue.
She said: "This has now been going on for so long, we are deeply frustrated and also deeply ashamed.
"I have to, in the morning, look myself in the mirror and say 'what have I done to actually make sure my Jewish friends do feel safe in the Labour party?' What am I doing?
"My membership of the Labour party is longer than Jeremy Corbyn's. I am steeped in the values, the ethic, the morality of Labour values and these offend my Labour values fundamentally."
She added that the Lords have tried to deal with the issue internally but that they "really do feel that we've been letting down the younger people in the party".
The peers also accuse Mr Corbyn of not having “opened (his) eyes” or “accepted responsibility” for the row which has engulfed the party.
“We can’t be a credible alternative government that will bring the country together if we can’t get our own house in order,” the advert says.
“Your failure to do the right thing will lead to the failure of the Labour Party being able to make our country a better place for the people and communities we seek to serve.”
“You have failed to defend our party’s anti-racist values,” it adds.
“You have therefore failed the test of leadership.”
Addressing Mr Corbyn directly, the advert states: “The Labour party welcomes everyone* irrespective of race, creed, age, gender identity, or sexual orientation. (*except, it seems, Jews). This is your legacy Mr Corbyn.”
The Labour leader has faced mounting pressure since the Panorama programme, which claimed that senior figures, including Mr Corbyn’s communications chief Seumas Milne and general secretary Jennie Formby, had interfered in anti-Semitism investigations.
Labour has denied the claims and written a complaint to the BBC.
Lord Harris of Haringey, chairman of the Labour Peers Group, said on Tuesday that Mr Corbyn was “not cut out” to be a party leader, while Tory leadership hopefuls Boris Johnson and Jeremy Hunt have suggested Mr Corbyn may be anti-Semitic – a claim described as a “baseless political attack” by Labour.
Labour peers have already offered to investigate allegations of anti-Semitism in the party and warned Mr Corbyn that without full openness it was “a cancer that will continue to grow”.
Meanwhile, Labour’s governing body has been urged to support a motion which would automatically exclude members where there is “irrefutable evidence” accusing them of racism and other forms of discrimination.
Tom Watson, the party’s deputy leader, was among five members of the National Executive Committee who submitted the motion to the chair of the NEC.
The proposed change, which will be debated at a meeting next Tuesday, calls on the NEC to bring forward forward rule changes to the annual conference.