Mutually-owned Co-operative blamed the deteriorating economic outlook for its decision to drop its £750m bid and said it was "disappointed" by the loss of an opportunity to massively increase its small presence in Scotland.
Part-nationalised Lloyds will now ask European competition officials to extend the deadline for the divestment, which is due by November, into 2014.
It will press on with plans to rebrand the business as TSB Bank this summer.
Peter Marks, Co-operative Group's chief executive, said: "Against the backdrop of the current economic environment, the worsened outlook for economic growth and the increasing regulatory requirements on the financial services sector in general, the Verde transaction would not currently deliver a suitable return for our members within a reasonable timeframe and with an acceptable level of risk."
The collapse of the deal is a massive blow to Co-operative's plan to expand in Scotland.
Co-operative currently has just one bank branch and three outlets of its Britannia business in Scotland.
Verde would have handed it 185 Lloyds TSB Scotland branches plus four that operate as Cheltenham & Gloucester, giving it the country's third-biggest branch network.
A Co-operative spokesman said: "From a Scottish perspective we are disappointed. We do not have enough presence north of the Border. We saw Verde as an opportunity to address that."
The Co-operative will continue to pursue plans to sell its general insurance business as the group prepares to welcome Scot Euan Sutherland as its new chief executive.
In 2012 alone, Lloyds spent £570m on the Verde divestment and Co-operative £38.5m.
Lloyds, which is 41% owned by the taxpayer, has estimated that selling Verde, headed by former Virgin Money and Santander executive Paul Pester, will cost it around £1 billion after tax.
Conducting an initial public offering for the business could add to that bill.
Lloyds chief executive Antonio Horta-Osorio said: "We are dis-appointed that the Co-operative Group is unable to complete this transaction.
"However, we are well advanced in our plans to bring the Verde business to the UK high street during the summer through the TSB Bank, and will now proceed with the option to IPO the business, subject to the necessary approvals.
"The TSB Bank will be an attractive retail and commercial bank that will have around 630 branches across the UK, a strong management team and will be a real challenger on the high street."
The sale of the 632-strong branch network was demanded by the European Commission as a condition of Lloyds receiving state aid in the wake of the financial crisis and its acquisition of Edinburgh-based Halifax Bank of Scotland.
Around 7500 workers will be part of the divestment, including more than 2000 employees in Scotland.
Dominic Hook, national officer of trade union Unite, said: "The staff at the branches, which are up for sale, will be very anxious – they need certainty.
"Unite is calling on the Government and Lloyds to do everything possible to create options that will support UK banking, give customers choice and protect staff.
"The last thing staff and customers need is a fire sale of the branches, which could lead to them falling into the wrong hands."
The city's reaction was muted, with shares rising 0.9p to 52p.
Gary Greenwood, of Shore Capital, said: "The terms of the sale to the Co-op were fairly onerous to Lloyds, in our opinion, so this could actually be good news for Lloyds shareholders."
November 2009: European Commission orders Lloyds to sell businesses including Lloyds TSB Scotland.
May 2011: Confirmation that Lloyds TSB Scotland will be sold as package with other "Project Verde" businesses.
December 2011: Co-operative Bank named preferred bidder.
April 2012: NBNK tables fresh bid.
July 2012: Heads of terms signed with Co-operative.
April 2013 Co-operative deal collapses.
Summer 2013: Verde business to start operating as TSB.
November 2013: Deadline for sale.