Mr Daniels will lose £580,000 after his original £1.45m bonus was cut by 40%.
Bonuses for another four directors will be cut by £190,000 to £260,000, while a further eight executives will receive about £100,000 less.
They are being penalised for the bank's mis-selling of payment protection insurance (PPI).
In theory,  PPI covered repayments if borrowers were unable to keep them up, promising help during illness or unemployment, but in many cases, those taking out the policies would not have been eligible to claim on them.
Lloyds has been forced to set aside £3.2bn to cover compensation for those customers who were mis-sold PPI.
Lloyds said in a statement that it would make an adjustment to a proportion of the bonus awards for 2010, because if it had been aware of the mis-selling and the cost of putting it right, the bonus pool and the awards from it would have been smaller.
By Robert PestonBusiness editor
The cut will be made by reducing the amounts already awarded in deferred shares.
Bonuses for 2011 will also be lower than planned.
This is the first time a British bank has taken back bonuses from executives, following a financial performance that was worse than expected.
The return of some of the bonuses, which were demanded by regulators after the banking crisis of 2008, are being made after pressure from politicians and the Financial Services Authority.
Lloyds Banking Group is the UK's biggest lender and owns the Halifax, the Bank of Scotland and the Cheltenham and Gloucester.
The bank will publish its results this Friday and is expected to announce a loss of about £3.5bn.
Its current chief executive, Antonio Horta-Osorio, said in January he would not take an annual bonus for 2011.
Our business editor says the retrospective cut in these bonuses may have a deterrent effect in future, making bankers more likely to consider the consequences when they launch new products or do assorted deals.
Chris Skinner, the chairman of the Financial Services Club, said: "It will be interesting to see if other banks follow this lead."
Lloyds Banking Group has confirmed it is cutting £2m from bonuses paid to 13 executives, including the former chief executive Eric Daniels.