"This will be a unique opportunity to accelerate and extend our strategy and create the UK's leading financial services group," said Lloyds chairman Sir Victor Blank.
Lloyds chief executive Eric Daniels said "You have the largest savings bank, you have the largest current account provider, you have two terrific distribution networks."
According to the deal agreement "significant cost savings can be made by combining the networks and back offices of Lloyds TSB and HBOS".
Under the cost saving plan retail branches will be cut, while head office posts, human resources and finance and legal departments will also face cuts.
Analysts have suggested that up to 40,000 jobs could go, but banking consultant Jonathan Charley said HBOS was under pressure not to make such deep cuts.
He estimated that 10% of the combined workforce, or about 14,000 posts, could be cut.
BBC business editor Robert Peston said the government had opted to push through the Lloyds TSB-HBOS tie-up after HBOS voiced concerns that depositors and lenders had begun to withdraw their credit from the bank.
Declan Curry goes through the main points of the deal
Earlier Chancellor Alistair Darling said the government would allow the HBOS-Lloyds TSB deal because financial stability "must trump" competition fears.
But he denied that the authorities had rushed through the transaction.
"It didn't just suddenly happen," he told the BBC.
City watchdog, the Financial Services Authority (FSA) welcomed the merger saying it would "enhance stability within financial markets and improve confidence among customers and investors in the UK financial sector".
Concerns about HBOS's security were so great that even the prime minister was involved in pushing through the deal, our business editor said.
"There were growing concerns in the HBOS boardroom that a climate of fear was being created about its future that could have led to a funding crisis, or a Northern Rock-style run - on steroids," he said.
Meanwhile, Mr Daniels - who will take over the helm of the new firm - was keen to stress that the takeover had not been forced on HBOS.
"There shouldn't be any impression this is a shotgun marriage or a forced marriage, this is something that's been looked at for a good long while," he said.
This is the right transaction for HBOS and its shareholders
Lloyds added that the takeover was part of its strategy to build "the UK's leading finance company", adding that it also intends to increase the number of competitive mortgages on offer for first-time home buyers.
The creation of such a large bank, which will hold a third of the UK mortgage and savings market, would not normally be allowed under competition rules say analysts.
But the deal was backed by the government, using a special national interest clause, on the grounds that a collapse of HBOS would have had a disastrous impact on the UK.
However, Lloyds chairman Sir Victor Blank did say the Office of Fair Trading would look "very carefully" at the business if it discovered any market abuses in the future.
The group also moved to allay fears that the takeover would mean a blow to Scotland where HBOS is currently based.
Lloyds said the new group would continue to use The Mound - HBOS's corporate headquarters - in Scotland, continue to hold annual general meetings in Scotland and carry on printing Bank of Scotland notes.
"In addition the management's focus is to keep jobs in Scotland," it added.
HBOS chief Andy Hornby will remain with the company, but his role has not been decided.
"Against the backdrop of the very high levels of volatility our industry is experiencing, the combined group will be one of the strongest players in the UK financial services sector.
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