The offer of 5 per cent, which came after intensive negotiations at the conciliation service Acas, will also affect wage negotiations elsewhere in industry at a time when most settlements are being struck at around 3 per cent.
It is thought the relatively generous deal is an attempt to pave the way for the smooth integration of the pay systems of the old Lloyds and TSB banks and to avoid the threat of industrial action.
The move also comes ahead of the bank's results on Friday, expected to show record pre-tax profits of around pounds 2.5bn.
The Banking, Insurance and Finance Union gave a guarded welcome to the pay offer because it means the overwhelming majority of employees will in effect receive 5 per cent, despite a trend towards individual performance- related pay.
Only around 100 employees, rated the least efficient by management, will get no increase, while a relatively few staff on the very highest performance grades, will enjoy a rise of 6 or 7 per cent.
John Townsend, assistant secretary at the union, also pointed out that the package gave little leeway for local pay based on labour market conditions, and managers would therefore have less potentially unfair power over what their subordinates earned. Under the proposals, all staff will move to non-contributory pensions.
Mr Townsend, however, said Lloyds TSB might well return to the negotiating table next year with fresh proposals on merit pay and localised salaries and called on management to agree a central pay policy. The staff appraisal systems should be properly integrated and the union would seek to enhance the earnings of those on the lowest rates.
It is thought unlikely that the bank's employees will now vote for industrial action if the union decides to press ahead with a ballot.
The other main banks have also yet to settle. There is no offer at Barclays, at Midland a claim has just been submitted, while at NatWest management has offered a 3 per cent increase on the pay bill, but with substantial individual differences based on performance.
Mr Townsend said the Lloyds TSB offer was an attempt to "sweeten the pill" of management proposals to merge the two workforces.
Employees were particularly incensed over management's plan to abolish preferential maternity leave arrangements enjoyed by TSB employees and bring them into line with Lloyds. Management may also be preparing the way for the possible closure of 650 branches with the loss of 10,000 jobs.
Last week the union delivered a legal petition to Parliament aimed at restricting the group's ability to cut its network of outlets.