TSB's takeover by Spanish bank Banco de Sabadell has been sealed after City regulators gave the £1.7 billion deal the green light.
Sabadell agreed to buy TSB earlier this year with aims to turn the bank into a major competitor to Britain's big five lenders.
Taxpayer-backed Lloyds Banking Group floated TSB last June after the brand was revived to meet the EU rules on state aid, but the return to the stock market proved short-lived with Sabadell making its takeover offer in March.
Lloyds said the deal's approval by the Prudential Regulation Authority and the Financial Conduct Authority means it has effectively completed the sale of its remaining 40% stake in the business for around £680 million.
It hopes to get confirmation that it has now met the European Commission's requirements on state aid "well ahead" of the year-end deadline.
Paul Pester, chief executive of TSB, said the deal was a "major vote of confidence in TSB".
He added: "With the extra fire-power and fresh perspective of Sabadell, TSB will be stronger and even better placed to build on its position as Britain's challenger bank."
Sabadell said completion of the deal marked a "milestone" for the group.
Chairman Josep Oliu said: "Today marks the beginning of a major project.
"This is a milestone that enables us to enter a market with vast opportunities. We do so in partnership with a well-positioned challenger bank with a prestigious brand backed by a long tradition."
TSB is the seventh largest retail bank in the UK, with more than 600 branches, 8,700 employees and 4.7 million customers.
But the group said in April it planned to close 17 branches and posted a sharp fall in first quarter profits - at £34.3 million, down 67% on a year ago.
TSB said the fall largely reflected higher costs, with operating expenses up as the group developed its infrastructure after being spun out of Lloyds and investment spending increased.
Lloyds was forced to offload TSB in return for its bailout at the height of the financial crisis.
The taxpayer was initially left holding a 40% stake in Lloyds, but this has since been reduced to less than 17% as the Government sells off tranches of shares with aims to return the bank to full private ownership.
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